Academic literature on the topic 'Local and $p$-adic fields'

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Journal articles on the topic "Local and $p$-adic fields"

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Li, Yin, and Hua Qiu. "p-adic Laplacian in local fields." Nonlinear Analysis: Theory, Methods & Applications 139 (July 2016): 131–51. http://dx.doi.org/10.1016/j.na.2016.02.025.

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LI, YIN. "WEIERSTRASS-TYPE FUNCTIONS IN p-ADIC LOCAL FIELDS." Fractals 28, no. 03 (May 2020): 2050043. http://dx.doi.org/10.1142/s0218348x20500437.

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The Weierstrass nowhere differentiable function has been studied often as example of functions whose graphs are fractals in [Formula: see text]. This paper investigates the Weierstrass-type function in the [Formula: see text]-adic local field [Formula: see text] whose graph is a repelling set of a discrete dynamical system, and proves that there exists a linear connection between the orders of the [Formula: see text]-adic calculus and the dimensions of the corresponding graphs.
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Qiu, Hua, and Weiyi Su. "3-Adic Cantor function on local fields and its p-adic derivative." Chaos, Solitons & Fractals 33, no. 5 (August 2007): 1625–34. http://dx.doi.org/10.1016/j.chaos.2006.03.024.

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Harari, David, and Tamás Szamuely. "Local-global questions for tori over $p$-adic function fields." Journal of Algebraic Geometry 25, no. 3 (March 31, 2016): 571–605. http://dx.doi.org/10.1090/jag/661.

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Mochizuki, Shinichi. "A Version of the Grothendieck Conjecture for p-Adic Local Fields." International Journal of Mathematics 08, no. 04 (June 1997): 499–506. http://dx.doi.org/10.1142/s0129167x97000251.

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Hua, Qiu, and Su Weiyi. "Weierstrass-like functions on local fields and their p-adic derivatives." Chaos, Solitons & Fractals 28, no. 4 (May 2006): 958–65. http://dx.doi.org/10.1016/j.chaos.2005.09.017.

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Scholze, Peter. "The Local Langlands Correspondence for GL n over p-adic fields." Inventiones mathematicae 192, no. 3 (August 11, 2012): 663–715. http://dx.doi.org/10.1007/s00222-012-0420-5.

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Seveso, Marco Adamo. "p-adic L-functions and the Rationality of Darmon Cycles." Canadian Journal of Mathematics 64, no. 5 (October 1, 2012): 1122–81. http://dx.doi.org/10.4153/cjm-2011-076-8.

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Abstract Darmon cycles are a higher weight analogue of Stark–Heegner points. They yield local cohomology classes in the Deligne representation associated with a cuspidal form on Γ0(N) of even weight k0 ≥ 2. They are conjectured to be the restriction of global cohomology classes in the Bloch–Kato Selmer group defined over narrow ring class fields attached to a real quadratic field. We show that suitable linear combinations of them obtained by genus characters satisfy these conjectures. We also prove p-adic Gross–Zagier type formulas, relating the derivatives of p-adic L-functions of the weight variable attached to imaginary (resp. real) quadratic fields to Heegner cycles (resp. Darmon cycles). Finally we express the second derivative of the Mazur– Kitagawa p-adic L-function of the weight variable in terms of a global cycle defined over a quadratic extension of ℚ.
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Gras, Georges. "Les θ-régulateurs locaux d'un nombre algébrique : Conjectures p-adiques." Canadian Journal of Mathematics 68, no. 3 (June 1, 2016): 571–624. http://dx.doi.org/10.4153/cjm-2015-026-3.

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AbstractLet K/ℚ be Galois and let η K ×be such that Reg∞(η)=0 .We define the local θ–regulator for the ℚp–irreducible characters θ of G = Gal(Kℚ). Let Vθ be the θ-irreducible representation. A linear representation is associated with whose nullity is equivalent to δ≥1. Each yields Regθp modulo p in the factorization of (normalized p–adic regulator). From Prob f ≥ 1 is a residue degree) and the Borel–Cantelli heuristic, we conjecture that for p large enough, RegGp(η) is a p–adic unit (a single with f = δ=1); this obstruction may be led assuming the existence of a binomial probability law confirmed through numerical studies (groups C3, C5, D6) is conjecture would imply that for all p large enough, Fermat quotients, normalized p–adic regulators are p–adic units and that number fields are p-rational.We recall some deep cohomological results that may strengthen such conjectures.
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Bocardo-Gaspar, Miriam, Hugo García-Compeán, Edgar Y. López, and Wilson A. Zúñiga-Galindo. "Local Zeta Functions and Koba–Nielsen String Amplitudes." Symmetry 13, no. 6 (May 29, 2021): 967. http://dx.doi.org/10.3390/sym13060967.

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This article is a survey of our recent work on the connections between Koba–Nielsen amplitudes and local zeta functions (in the sense of Gel’fand, Weil, Igusa, Sato, Bernstein, Denef, Loeser, etc.). Our research program is motivated by the fact that the p-adic strings seem to be related in some interesting ways with ordinary strings. p-Adic string amplitudes share desired characteristics with their Archimedean counterparts, such as crossing symmetry and invariance under Möbius transformations. A direct connection between p-adic amplitudes and the Archimedean ones is through the limit p→1. Gerasimov and Shatashvili studied the limit p→1 of the p-adic effective action introduced by Brekke, Freund, Olson and Witten. They showed that this limit gives rise to a boundary string field theory, which was previously proposed by Witten in the context of background independent string theory. Explicit computations in the cases of 4 and 5 points show that the Feynman amplitudes at the tree level of the Gerasimov–Shatashvili Lagrangian are related to the limit p→1 of the p-adic Koba–Nielsen amplitudes. At a mathematical level, this phenomenon is deeply connected with the topological zeta functions introduced by Denef and Loeser. A Koba–Nielsen amplitude is just a new type of local zeta function, which can be studied using embedded resolution of singularities. In this way, one shows the existence of a meromorphic continuations for the Koba–Nielsen amplitudes as functions of the kinematic parameters. The Koba–Nielsen local zeta functions are algebraic-geometric integrals that can be defined over arbitrary local fields (for instance R, C, Qp, Fp((T))), and it is completely natural to expect connections between these objects. The limit p tends to one of the Koba–Nielsen amplitudes give rise to new amplitudes which we have called Denef–Loeser amplitudes. Throughout the article, we have emphasized the explicit calculations in the cases of 4 and 5 points.
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Dissertations / Theses on the topic "Local and $p$-adic fields"

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Miller, Justin Thomson. "On p-adic Continued Fractions and Quadratic Irrationals." Diss., The University of Arizona, 2007. http://hdl.handle.net/10150/194074.

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In this dissertation we investigate prior definitions for p-adic continued fractions and introduce some new definitions. We introduce a continued fraction algorithm for quadratic irrationals, prove periodicity for Q₂ and Q₃, and numerically observe periodicity for Q(p) when p < 37. Various observations and calculations regarding this algorithm are discussed, including a new type of symmetry observed in many of these periods, which is different from the palindromic symmetry observed for real continued fractions and some previously defined p-adic continued fractions. Other results are proved for p-adic continued fractions of various forms. Sufficient criteria are given for a class of p-adic continued fractions of rational numbers to be finite. An algorithm is given which results in a periodic continued fraction of period length one for √D ∈ Zˣ(p), D ∈ Z, D non-square; although, different D require different parameters to be used in the algorithm. And, a connection is made between continued fractions and de Weger’s approximation lattices, so that periodic continued fractions can be generated from a periodic sequence of approximation lattices, for square roots in Zˣ(p). For simple p-adic continued fractions with rational coefficients, we discuss observations and calculations related to Browkin’s continued fraction algorithms. In the last chapter, we apply some of the definitions and techniques developed in the earlier chapters for Q(p) and Z to the t-adic function field case F(q)((t)) and F(q)[t], respectively. We introduce a continued fraction algorithm for quadratic irrationals in F(q)((t)) that always produces periodic continued fractions.
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Chinner, Trinity. "Elliptic Tori in p-adic Orthogonal Groups." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42759.

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In this thesis, we classify up to conjugacy the maximal elliptic toral subgroups of all special orthogonal groups SO(V), where (q,V) is a 4-dimensional quadratic space over a non-archimedean local field of odd residual characteristic. Our parameterization blends the abstract theory of Morris with a generalization of the practical work performed by Kim and Yu for Sp(4). Moreover, we compute an explicit Witt basis for each such torus, thereby enabling its concrete realization as a set of matrices embedded into the group. This work can be used explicitly to construct supercuspidal representations of SO(V).
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Jondreville, David. "Quantification de groupes p-adiques et applications aux algèbres d'opérateurs." Thesis, Reims, 2017. http://www.theses.fr/2017REIMS010.

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Cette thèse est consacrée à l'étude des déformations des C*-algèbres munies d'une action de groupe, du point de vue de la quantification équivariante non-formelle, dans le cas non-archimédien. Nous construisons une théorie de déformation des C*-algèbres munies d'une action d'un espace vectoriel de dimension finie sur un corps local non-archimédien de caractéristique différente de 2 ainsi que pour des quotients du groupe affine d'un corps local dont le corps résiduel est de cardinal impair. Par ailleurs, nous construisons des familles de 2-cocycles unitaires afin de déformer des groupes quantiques localement compacts agissant sur ces C*-algèbres déformées
This thesis is devoted to the study of deformation of C*-algebras endowed with a group action, from the perspective of non-formal equivariant quantization, in the non-Archimedean setting. We construct a deformation theory of C*-algebras endowed with an action of a finite dimensional vector space over a non-Archimedean local field of characteristic different from 2 and for quotients of the affine group of a local field whose residue field has cardinality not divisible by 2. Moreover, we construct families of dual unitary 2-cocycles in order to deform locally compact quantum groups acting on these deformed C*-algebras
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Sordo, Vieira Luis A. "ON P-ADIC FIELDS AND P-GROUPS." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/43.

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The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal forms. The second part deals with the theory of finite groups. We treat computations of Chermak-Delgado lattices of p-groups. We compute the Chermak-Delgado lattices for all p-groups of order p^3 and p^4 and give results on p-groups of order p^5.
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Malon, Christopher D. "The p-adic local langlands conjecture." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33667.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (leaves 46-47).
Let k be a p-adic field. Split reductive groups over k can be described up to k- isomorphism by a based root datum alone, but other groups, called rational forms of the split group, involve an action of the Galois group of k. The Galois action on the based root datum is shared by members of an inner class of k-groups, in which one k--isomorphism class is quasi-split. Other forms of the inner class can be called pure or impure, depending on the Galois action. Every form of an adjoint group is pure, but only the quasi-split forms of simply connected groups are pure. A p-adic Local Langlands correspondence would assign an L-packet, consisting of finitely many admissible representations of a p-adic group, to each Langlands parameter. To identify particular representations, data extending a Langlands parameter is needed to make "completed Langlands parameters." Data extending a Langlands parameter has been utilized by Lusztig and others to complete portions of a Langlands classification for pure forms of reductive p- adic groups, and in applications such as endoscopy and the trace formula, where an entire L-packet of representations contributes at once.
(cont.) We consider a candidate for completed Langlands parameters to classify representations of arbitrary rational forms, and use it to extend a classification of certain supercuspidal representations by DeBacker and Reeder to include the impure forms.
by Christopher D. Malon.
Ph.D.
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Ramero, Lorenzo. "An ℓ-adic Fourier transform over local fields." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28040.

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Chojecki, Przemyslaw. "P-adic local Langlands correspondence and geometry." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066035/document.

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Cette these concerne la geometrie de la correspondance de Langlands p-adique. On donne la formalisation des methodes de Emerton, qui permettrait d'etablir la conjecture de Fontaine-Mazur dans le cas general des groupes unitaires. Puis, on verifie que ce formalism est satisfait dans la cas de U(3) ou on utilise la construction de Breuil-Herzig pour la correspondence p-adique. De point de vue local, on commence l'etude de cohomologie modulo p et p-adiques de tour de Lubin-Tate pour GL_2(Q_p). En particulier, on demontre que on peut retrouver la correspondence de Langlands p-adique dans la cohomologie completee de tour de Lubin-Tate
This thesis concerns the geometry behind the p-adic local Langlands correspondence. We give a formalism of methods of Emerton, which would permit to establish the Fontaine-Mazur conjecture in the general case for unitary groups. Then, we verify that our formalism works well in the case of U(3) where we use the construction of Breuil-Herzig as the input for the p-adic correspondence.From the local viewpoint, we start a study of the modulo p and p-adic cohomology of the Lubin-Tate tower for GL_2(Q_p). In particular, we show that we can find the local p-adic Langlands correspondence in the completed cohomology of the Lubin-Tate tower
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Aubertin, Bruce Lyndon. "Algebraic numbers and harmonic analysis in the p-series case." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/30282.

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For the case of compact groups G = Π∞ j=l Z(p)j which are direct products of countably many copies of a cyclic group of prime order p, links are established between the theories of uniqueness and spectral synthesis on the one hand, and the theory of algebraic numbers on the other, similar to the well-known results of Salem, Meyer et al on the circle. Let p ≥ 2 be a prime and let k{x⁻¹} denote the p-series field of formal Laurent series z = Σhj=₋∞ ajxj with coefficients in the field k = {0, 1,…, p-1} and the integer h arbitrary. Let L(z) = - ∞ if aj = 0 for all j; otherwise let L(z) be the largest index h for which ah ≠ 0. We examine compact sets of the form [Algebraic equation omitted] where θ ε k{x⁻¹}, L(θ) > 0, and I is a finite subset of k[x]. If θ is a Pisot or Salem element of k{x⁻¹}, then E(θ,I) is always a set of strong synthesis. In the case that θ is a Pisot element, more can be proved, including a version of Bochner's property leading to a sharper statement of synthesis, provided certain assumptions are made on I (e.g., I ⊃ {0,1,x,...,xL(θ)-1}). Let G be the compact subgroup of k{x⁻¹} given by G = {z: L(z) < 0}. Let θ ɛ k{x⁻¹}, L(θ) > 0, and suppose L(θ) > 1 if p = 3 and L(θ) > 2 if p = 2. Let I = {0,1,x,...,x²L(θ)-1}. Then E = θ⁻¹Ε(θ,I) is a perfect subset of G of Haar measure 0, and E is a set of uniqueness for G precisely when θ is a Pisot or Salem element. Some byways are explored along the way. The exact analogue of Rajchman's theorem on the circle, concerning the formal multiplication of series, is obtained; this is new, even for p = 2. Other examples are given of perfect sets of uniqueness, of sets satisfying the Herz criterion for synthesis, and sets of multiplicity, including a class of M-sets of measure 0 defined via Riesz products which are residual in G. In addition, a class of perfect M₀-sets of measure 0 is introduced with the purpose of settling a question left open by W.R. Wade and K. Yoneda, Uniqueness and quasi-measures on the group of integers of a p-series field, Proc. A.M.S. 84 (1982), 202-206. They showed that if S is a character series on G with the property that some subsequence {SpNj} of the pn-th partial sums is everywhere pointwise bounded on G, then S must be the zero series if SpNj → 0 a.e.. We obtain a strong complement to this result by establishing that series S on G exist for which Sn → 0 everywhere outside a perfect set of measure 0, and for which sup |SpN| becomes unbounded arbitrarily slowly.
Science, Faculty of
Mathematics, Department of
Graduate
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Breuning, Manuel. "Equivariant epsilon constants for Galois extensions of number fields and P-adic fields." Thesis, King's College London (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409402.

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Minardi, John. "Iwasawa modules for [p-adic]-extensions of algebraic number fields /." Thesis, Connect to this title online; UW restricted, 1986. http://hdl.handle.net/1773/5742.

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Books on the topic "Local and $p$-adic fields"

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1937-, Doran Robert S., Sally Paul, and Spice Loren 1981-, eds. Harmonic analysis on reductive, p-adic groups: AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups, January 16, 2010, San Francisco, CA. Providence, R.I: American Mathematical Society, 2011.

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International Conference on p-Adic Functional Analysis (11th 2010 Université Blaise Pascal). Advances in non-Archimedean analysis: Eleventh International Conference on p-Adic Functional Analysis, July 5-9 2010, Université Blaise Pascal, Clermont-Ferrand, France. Edited by Araujo-Gomez Jesus 1965-, Diarra B. (Bertin) 1944-, and Escassut Alain. Providence, R.I: American Mathematical Society, 2011.

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1971-, Orlik Sascha, and Rapoport M. 1948-, eds. Period domains over finite and p-adic fields. Cambridge: Cambridge University Press, 2010.

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Germany) International Conference on p-adic Functional Analysis (13th 2014 Paderborn. Advances in non-Archimedean analysis: 13th International Conference on p-adic Functional Analysis, August 12-16, 2014, University of Paderborn, Paderborn, Germany. Edited by Glöckner Helge 1969 editor, Escassut Alain editor, and Shamseddine Khodr 1966 editor. Providence, Rhode Island: American Mathematical Society, 2016.

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Colmez, Pierre. Intégration sur les variétés p-adiques. Paris: Société Mathématique de France, 1998.

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Colmez, Pierre. Intégration sur les variétés p-adiques. Paris: Société Mathématique de France, 1998.

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Chuong, Nguyen Minh. Pseudodifferential Operators and Wavelets over Real and p-adic Fields. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77473-2.

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Grob, Camilla. Die Entscheidbarkeit der Theorie der maximalen pseudo p-adisch abgeschlossenen Körper. Konstanz: Hartung-Gorre, 1987.

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International Conference on p-Adic and Non-Archimedean Analysis (10th 2008 Michigan State University). Advances in p-adic and non-Archimedean analysis: Tenth International Conference on p-Adic and Non-Archimedean Analysis, June 30-July 3, 2008, Michigan State University, East Lansing, Michigan. Edited by Berz M and Shamseddine Khodr 1966-. Providence, R.I: American Mathematical Society, 2010.

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M, Berz, and Shamseddine Khodr 1966-, eds. Advances in p-adic and non-Archimedean analysis: Tenth International Conference, June 30-July 3, 2008, Michigan State University, East Lansing, Michigan. Providence, R.I: American Mathematical Society, 2010.

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Book chapters on the topic "Local and $p$-adic fields"

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Narkiewicz, Władysław. "P-adic Fields." In Springer Monographs in Mathematics, 199–255. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-07001-7_5.

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Chuong, Nguyen Minh. "Wavelets on p-Adic Fields." In Pseudodifferential Operators and Wavelets over Real and p-adic Fields, 331–49. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77473-2_5.

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Deninger, Christopher, and Annette Werner. "Line Bundles and p-Adic Characters." In Number Fields and Function Fields—Two Parallel Worlds, 101–31. Boston, MA: Birkhäuser Boston, 2005. http://dx.doi.org/10.1007/0-8176-4447-4_7.

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Chuong, Nguyen Minh. "p-Adic Mathematical Analysis." In Pseudodifferential Operators and Wavelets over Real and p-adic Fields, 157–85. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77473-2_3.

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Chuong, Nguyen Minh. "Pseudodifferential Operators Over p-Adic Fields." In Pseudodifferential Operators and Wavelets over Real and p-adic Fields, 187–329. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77473-2_4.

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Robert, Alain M. "Construction of Universal p-adic Fields." In Graduate Texts in Mathematics, 127–59. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4757-3254-2_3.

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Hu, Pei-Chu, and Chung-Chun Yang. "Basic facts in p-adic analysis." In Meromorphic Functions over Non-Archimedean Fields, 1–31. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9415-8_1.

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Berndt, Rolf, and Ralf Schmidt. "Local Representations: The p-adic Case." In Progress in Mathematics, 105–36. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8772-4_5.

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Berndt, Rolf, and Ralf Schmidt. "Local Representations: The p-adic Case." In Elements of the Representation Theory of the Jacobi Group, 105–36. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0283-3_5.

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Gerstein, Larry. "Valuations, local fields, and 𝑝-adic numbers." In Graduate Studies in Mathematics, 51–79. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/090/03.

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Conference papers on the topic "Local and $p$-adic fields"

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Kaneko, Hiroshi. "Capacities and Function Spaces on the Local Field." In p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2193114.

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van der Put, Marius. "Local p-Adic Differential Equations." In p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2193131.

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Mijajlović, Žarko. "Infinitesimals in Nonstandard Analysis versus Infinitesimals in p-Adic Fields." In p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2193129.

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Kobayashi, Kazuyoshi, Rina Takada, and Takao Komatsu. "A note on periodicity of p-adic analytic functions." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841899.

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Dremov, V. "On the Chaotic Properties of Quadratic Maps Over Non-Archimedean Fields." In p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2193109.

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Suresh, V. "Quadratic Forms, Galois Cohomology and Function Fields of p-adic Curves." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0046.

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Izhboldin, Oleg. "p–primary part of the Milnor K–groups and Galois cohomologies of fields of characteristic p." In Higher local fields. Mathematical Sciences Publishers, 2000. http://dx.doi.org/10.2140/gtm.2000.3.19.

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Guepin, Florent, Christoph Haase, and James Worrell. "On the Existential Theories of Büchi Arithmetic and Linear p-adic Fields." In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2019. http://dx.doi.org/10.1109/lics.2019.8785681.

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Fesenko, Ivan. "Parshin's higher local class field theory in characteristic p." In Higher local fields. Mathematical Sciences Publishers, 2000. http://dx.doi.org/10.2140/gtm.2000.3.75.

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Rojas, J. Maurice, and Yuyu Zhu. "A Complexity Chasm for Solving Univariate Sparse Polynomial Equations Over p-adic Fields." In ISSAC '21: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3452143.3465554.

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