Relevant bibliographies by topics / Functions, Abelian

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Functions, Abelian'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 March 2023

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Journal articles on the topic "Functions, Abelian"

1

Rains, Eric M. "$BC_n$ -symmetric abelian functions." Duke Mathematical Journal 135, no. 1 (2006): 99–180. http://dx.doi.org/10.1215/s0012-7094-06-13513-5.

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Poinsot, Laurent. "Non Abelian bent functions." Cryptography and Communications 4, no. 1 (2011): 1–23. http://dx.doi.org/10.1007/s12095-011-0058-y.

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CHO, KOJI, and ATSUSHI NAKAYASHIKI. "DIFFERENTIAL STRUCTURE OF ABELIAN FUNCTIONS." International Journal of Mathematics 19, no. 02 (2008): 145–71. http://dx.doi.org/10.1142/s0129167x08004595.

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The space of Abelian functions of a principally polarized abelian variety (J,Θ) is studied as a module over the ring [Formula: see text] of global holomorphic differential operators on J. We construct a [Formula: see text] free resolution in case Θ is non-singular. As an application, in the case of dimensions 2 and 3, we construct a new linear basis of the space of abelian functions which are singular only on Θ in terms of logarithmic derivatives of the higher-dimensional σ-function.
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Müller, L. Felipe. "Rational $2$-functions are abelian." Communications in Number Theory and Physics 15, no. 3 (2021): 605–14. http://dx.doi.org/10.4310/cntp.2021.v15.n3.a5.

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ŁUKASIK, RADOSŁAW. "-SPHERICAL FUNCTIONS ON ABELIAN SEMIGROUPS." Bulletin of the Australian Mathematical Society 96, no. 3 (2017): 479–86. http://dx.doi.org/10.1017/s0004972717000417.

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We present the form of the solutions $f:S\rightarrow \mathbb{C}$ of the functional equation $$\begin{eqnarray}\mathop{\sum }_{\unicode[STIX]{x1D706}\in K}f(x+\unicode[STIX]{x1D706}y)=|K|f(x)f(y)\quad \text{for }x,y\in S,\end{eqnarray}$$ where $f$ satisfies the condition $f(\sum _{\unicode[STIX]{x1D706}\in K}\unicode[STIX]{x1D706}x)\neq 0$ for all $x\in S$, $(S,+)$ is an abelian semigroup and $K$ is a subgroup of the automorphism group of $S$.
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MA, WU-XIA, and YONG-GAO CHEN. "REPRESENTATION FUNCTIONS ON ABELIAN GROUPS." Bulletin of the Australian Mathematical Society 99, no. 1 (2018): 10–14. http://dx.doi.org/10.1017/s0004972718000783.

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Let$G$be a finite abelian group,$A$a nonempty subset of$G$and$h\geq 2$an integer. For$g\in G$, let$R_{A,h}(g)$denote the number of solutions of the equation$x_{1}+\cdots +x_{h}=g$with$x_{i}\in A$for$1\leq i\leq h$. Kisset al. [‘Groups, partitions and representation functions’,Publ. Math. Debrecen85(3) (2014), 425–433] proved that (a) if$R_{A,h}(g)=R_{G\setminus A,h}(g)$for all$g\in G$, then$|G|=2|A|$, and (b) if$h$is even and$|G|=2|A|$, then$R_{A,h}(g)=R_{G\setminus A,h}(g)$for all$g\in G$. We prove that$R_{G\setminus A,h}(g)-(-1)^{h}R_{A,h}(g)$does not depend on$g$. In particular, if$h$is even and$R_{A,h}(g)=R_{G\setminus A,h}(g)$for some$g\in G$, then$|G|=2|A|$. If$h>1$is odd and$R_{A,h}(g)=R_{G\setminus A,h}(g)$for all$g\in G$, then$R_{A,h}(g)=\frac{1}{2}|A|^{h-1}$for all$g\in G$. If$h>1$is odd and$|G|$is even, then there exists a subset$A$of$G$with$|A|=\frac{1}{2}|G|$such that$R_{A,h}(g)\not =R_{G\setminus A,h}(g)$for all$g\in G$.
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Buchstaber, V. M., V. Z. Enolskii, and D. V. Leykin. "Rational analogs of abelian functions." Functional Analysis and Its Applications 33, no. 2 (1999): 83–94. http://dx.doi.org/10.1007/bf02465189.

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Schmidt, Maximilian. "Seshadri functions on abelian surfaces." Advances in Mathematics 413 (January 2023): 108827. http://dx.doi.org/10.1016/j.aim.2022.108827.

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Ritter, Jurgen, and Alfred Weiss. "Non-abelian Pseudomeasures and Congruences between Abelian Iwasawa L-functions." Pure and Applied Mathematics Quarterly 4, no. 4 (2008): 1085–106. http://dx.doi.org/10.4310/pamq.2008.v4.n4.a5.

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Kaarli, Kalle, and László Márki. "Endoprimal abelian groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 67, no. 3 (1999): 412–28. http://dx.doi.org/10.1017/s1446788700002093.

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AbstractA group A is said to be endoprimal if its term functions are precisely the functions which permute with all endomorphisms of A. In this paper we describe endoprimal groups in the following three classes of abelian groups: torsion groups, torsionfree groups of rank at most 2, direct sums of a torsion group and a torsionfree group of rank 1.
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Dissertations / Theses on the topic "Functions, Abelian"

1

England, Matthew. "Higher genus Abelian functions associated with algebraic curves." Thesis, Heriot-Watt University, 2009. http://hdl.handle.net/10399/2301.

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We investigate the theory of Abelian functions with periodicity properties defined from an associated algebraic curve. A thorough summary of the background material is given, including a synopsis of elliptic function theory, generalisations of the Weierstrass σ and 0functions and a literature review. The theory of Abelian functions associated with a tetragonal curve of genus six is considered in detail. Differential equations and addition formula satisfied by the functions are derived and a solution to the Jacobi Inversion Problem is presented. New methods which centre on a series expansion of the σ function are used and discussions on the large computations involved are included. We construct a solution to the KP equation using these functions and outline how a general class of solutions can be generated from a wider class of curves. We proceed to present new approaches used to complete results for the lower genus trigonal curves. We also give some details on the the theory of higher genus trigonal curves before finishing with an application of the theory to the Benney moment equations. A reduction is constructed corresponding to Schwartz-Christoffel maps associated with the tetragonal curve. The mapping function is evaluated explicitly using derivatives of the σ function.
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Dokchitser, Vladimir. "L-functions of non-abelian twists of elliptic curves." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615194.

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Barker, Russell. "L#kappa#-equivalence and Hanf functions for finite structures." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270249.

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Attwell-Duval, Dylan. "Evaluating zeta functions of Abelian number fields at negative integers." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=92404.

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In this thesis we study abelian number fields and in particular their zeta functions at the negative integers. The prototypical examples of abelian number fields are the oft-studied cyclotomic fields, a topic upon which many texts have been almost exclusively dedicated to (see for example \cite{washington1997introduction} or nearly any text on global class field theory). \\ We begin by building up our understanding of the characters of finite abelian groups and how they are related to Dedekind zeta functions. We then use tools from number theory such as the Kronecker-Weber theorem and Bernoulli numbers to find a simple algorithm for determining the values of these zeta functions at negative integers. We conclude the thesis by comparing the relative complexity of our method to two alternative methods that use completely different theoretical tools to attack the more general problem of non-abelian number fields.<br>Dans cette thèse nous étudions les corps de nombres abéliens et en particulier leurs fonctions zeta aux entiers négatifs. Les exemples-type de corps de nombres abéliens sont les corps cyclotomiques que l'on étudie fréquemment, un sujet auquel de nombreux textes ont été entièrement consacrés (voir par exemple \cite{washington1997introduction} ou presque tous les textes sur la théorie globale des corps de classes).<br>Nous commençons par construire notre comprehension des caractères des groupes abéliens finis et de ce qui les lie aux fonctions zeta de Dedekind. Ensuite nous utilisons des outils de théorie des nombres comme le théorème de Kronecker-Weber et les nombres de Bernouilli pour trouver un algorithme simple pour déterminer les valeurs de ces fonctions zeta aux entiers négatifs. Nous concluons la thèse en comparant la complexité relative de notre méthode a deux méthodes alternatives qui utilisent des outils théoriques complètement différents pour attaquer le problème plus général des corps de nombres non-abéliens.
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Grant, David R. MD FRCSC. "Theta functions and division points on Abelian varieties of dimension two." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/115469.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1985.<br>MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.<br>Bibliography: leaves 123-124.<br>by David R. Grant.<br>Ph.D.
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Sumi, Ken. "Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263432.

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Robert, Damien. "Fonction thêta et applications à la cryptographie." Thesis, Nancy 1, 2010. http://www.theses.fr/2010NAN10037/document.

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Le logarithme discret sur les courbes elliptiques fournit la panoplie standard de la cryptographie à clé publique: chiffrement asymétrique, signature, authentification. Son extension à des courbes hyperelliptiques de genre supérieur se heurte à la difficulté de construire de telles courbes qui soient sécurisées. Dans cette thèse nous utilisons la théorie des fonctions thêta développée par Mumford pour construire des algorithmes efficaces pour manipuler les variétés abéliennes. En particulier nous donnons une généralisation complète des formules de Vélu sur les courbes elliptiques pour le calcul d'isogénie sur des variétés abéliennes. Nous donnons également un nouvel algorithme pour le calcul efficace de couplage sur les variétés abéliennes en utilisant les coordonnées thêta. Enfin, nous présentons une méthode de compression des coordonnées pour améliorer l'arithmétique sur les coordonnées thêta de grand niveau. Ces applications découlent d'une analyse fine des formules d'addition sur les fonctions thêta. Si les résultats de cette thèse sont valables pour toute variété abélienne, pour les applications nous nous concentrons surtout sur les jacobienne de courbes hyperelliptiques de genre~$2$, qui est le cas le plus significatif cryptographiquement<br>The discrete logarithm on elliptic curves give the standard protocols in public key cryptography: asymmetric encryption, signatures, ero-knowledge authentification. To extends the discrete logarithm to hyperelliptic curves of higher genus we need efficient methods to generate secure curves. The aim of this thesis is to give new algorithms to compute with abelian varieties. For this we use the theory of algebraic theta functions in the framework of Mumford. In particular, we give a full generalization of Vélu's formulas for the computation of isogenies on abelian varieties. We also give a new algorithm for the computation of pairings using theta coordinates. Finally we present a point compression method to manipulate These applications follow from the analysis of Riemann relations on theta functions for the addition law. If the results of this thesis are valid for any abelian variety, for the applications a special emphasis is given to Jacobians of hyperelliptic genus~$2$ curves, since they are the most significantly relevant case in cryptography
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Haloui, Safia-Christine. "Sur le nombre de points rationels des variétés abéliennes sur les corps finis." Thesis, Aix-Marseille 2, 2011. http://www.theses.fr/2011AIX22038/document.

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Le polynôme caractéristique d'une variété abélienne sur un corps fini est défini comme étant celui de son endomorphisme de Frobenius. La première partie de cette thèse est consacrée à l'étude des polynômes caractéristiques de variétés abéliennes de petite dimension. Nous décrivons l'ensemble des polynômes intervenant en dimension 3 et 4, le problème analogue pour les courbes elliptiques et surfaces abéliennes ayant été résolu par Deuring, Waterhouse et Rück.Dans la deuxième partie, nous établissons des bornes supérieures et inférieures sur le nombre de points rationnels des variétés abéliennes sur les corps finis. Nous donnons ensuite des bornes inférieures spécifiques aux variétés jacobiennes. Nous déterminons aussi des formules exactes pour les nombres maximum et minimum de points rationnels sur les surfaces jacobiennes<br>The characteristic polynomial of an abelian variety over a finite field is defined to be the characteristic polynomial of its Frobenius endomorphism. The first part of this thesis is devoted to the study of the characteristic polynomials of abelian varieties of small dimension. We describe the set of polynomials which occur in dimension 3 and 4; the analogous problem for elliptic curves and abelian surfaces has been solved by Deuring, Waterhouse and Rück.In the second part, we give upper and lower bounds on the number of points on abelian varieties over finite fields. Next, we give lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces
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Pal, Aprameyo [Verfasser], and Otmar [Akademischer Betreuer] Venjakob. "Functional Equation of Characteristic Elements of Abelian Varieties over Function Fields / Aprameyo Pal ; Betreuer: Otmar Venjakob." Heidelberg : Universitätsbibliothek Heidelberg, 2013. http://d-nb.info/1177248506/34.

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Buyruk, Dilek. "On Algebraic Function Fields With Class Number Three." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613080/index.pdf.

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Let K/Fq be an algebraic function field with full constant field Fq and genus g. Then the divisor class number hK of K/Fq is the order of the quotient group, D0K /P(K), degree zero divisors of K over principal divisors of K. The classification of the function fields K with hK = 1 is done by MacRea, Leitzel, Madan and Queen and the classification of the extensions with class number two is done by Le Brigand. Determination of the necessary and the sufficient conditions for a function field to have class number three is done by H&uml<br>ulya T&uml<br>ore. Let k := Fq(T) be the rational function field over the finite field Fq with q elements. For a polynomial N &isin<br>Fq[T], we construct the Nth cyclotomic function field KN. Cyclotomic function fields were investigated by Carlitz, studied by Hayes, M. Rosen, M. Bilhan and many other mathematicians. Classification of cyclotomic function fields and subfields of cyclotomic function fields with class number one is done by Kida, Murabayashi, Ahn and Jung. Also the classification of function fields with genus one and classification of those with class number two is done by Ahn and Jung. In this thesis, we classified all algebraic function fields and subfields of cyclotomic function fields over finite fields with class number three.
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Books on the topic "Functions, Abelian"

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Baker, Henry Frederick. Abelian functions: Abel's theorem and the allied theory of theta functions. Cambridge University Press, 1995.

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Lang, Serge. Introduction to algebraic and abelian functions. 2nd ed. Springer-Verlag, 1995.

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Kempf, George. Complex abelian varieties and theta functions. Springer-Verlag, 1991.

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Kempf, George R. Complex abelian varieties and theta functions. Springer-Verlag, 1990.

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Kempf, George R. Complex Abelian Varieties and Theta Functions. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76079-2.

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1943-, Lange H., and Lange H. 1943-, eds. Complex Abelian varieties. 2nd ed. Springer, 2004.

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Adler, Allan. Moduli of Abelian varieties. Springer, 1996.

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Markushevich, A. I. Introduction to the classical theory of Abelian functions. American Mathematical Society, 1992.

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Landfriedt, E. Thetafunktionen und hyperelliptische funktionen. G. J. Göschen, 1990.

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Abelian varieties theta functions and the Fourier transforms. Cambridge University Press, 2003.

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Book chapters on the topic "Functions, Abelian"

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Freitag, Eberhard. "Abelian Functions." In Universitext. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20554-5_6.

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Wolfart, Jürgen, and Benjamin Mühlbauer. "Regular Dessins with Abelian Automorphism Groups." In From Arithmetic to Zeta-Functions. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28203-9_32.

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Fradkin, E. S., D. M. Gitman, and Sh M. Shvartsman. "Green’s Functions in Non-Abelian Theories." In Quantum Electrodynamics. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84258-0_8.

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André, Yves. "Endomorphisms in the Fibers of an Abelian Pencil." In G-Functions and Geometry. Vieweg+Teubner Verlag, 1989. http://dx.doi.org/10.1007/978-3-663-14108-2_11.

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Halle, Lars Halvard, and Johannes Nicaise. "Motivic Zeta Functions of Semi-Abelian Varieties." In Néron Models and Base Change. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26638-1_8.

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Weng, Lin. "Stability and New Non-Abelian Zeta Functions." In Developments in Mathematics. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3675-5_21.

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Hawkins, Thomas. "Abelian Functions: Problems of Hermite and Kronecker." In Sources and Studies in the History of Mathematics and Physical Sciences. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6333-7_10.

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Kakde, Mahesh. "Congruences Between Abelian p-Adic Zeta Functions." In Noncommutative Iwasawa Main Conjectures over Totally Real Fields. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32199-3_5.

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Nikolić-Despotović, Danica, and Stevan Pilipović. "Abelian Theorem for the Distributional Stieltjes Transformation." In Generalized Functions, Convergence Structures, and Their Applications. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-1055-6_13.

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Harder, G., and N. Schappacher. "Special values of hecke L-functions and abelian integrals." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0084583.

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Conference papers on the topic "Functions, Abelian"

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Aero, Eron L., Anatolii N. Bulygin, and Yurii V. Pavlov. "Nonlinear Klein-Fock-Gordon equation and Abelian functions." In Days on Diffraction 2013 (DD). IEEE, 2013. http://dx.doi.org/10.1109/dd.2013.6712794.

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Alkofer, Reinhard, Markus Huber, Valentin Mader, and Andreas Windisch. "On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge." In International Workshop on QCD Green's Functions, Confinement and Phenomenology. Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.136.0003.

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Stankovic, Radomir S., and Jaakko Astola. "Remarks on Bandwidth and Regularities in Functions on Finite Non-Abelian Groups." In 2008 38th International Symposium on Multiple Valued Logic (ismvl 2008). IEEE, 2008. http://dx.doi.org/10.1109/ismvl.2008.32.

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WENG, Lin. "Refined Brill-Noether Locus and Non-Abelian Zeta Functions for Elliptic Curves." In Proceedings of the Symposium. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705105_0011.

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Olejnik, Stefan, and Jeff Greensite. "Measuring the ground-state wave functional of SU(2) Yang-Mills theory in 3+1 dimensions: Abelian plane waves." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0467.

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