Relevant bibliographies by topics / Exponential sums

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

Academic literature on the topic 'Exponential sums'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Exponential sums"

1

Shparlinski, Igor E., and José Felipe Voloch. "Binomial exponential sums." ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE 21, no. 2 (December 2020): 931–41. http://dx.doi.org/10.2422/2036-2145.201811_007.

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Krätzel, Ekkehard. "DOUBLE EXPONENTIAL SUMS." Analysis 16, no. 2 (June 1996): 109–24. http://dx.doi.org/10.1524/anly.1996.16.2.109.

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Kerr, B. "INCOMPLETE EXPONENTIAL SUMS OVER EXPONENTIAL FUNCTIONS." Quarterly Journal of Mathematics 66, no. 1 (June 16, 2014): 213–24. http://dx.doi.org/10.1093/qmath/hau015.

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Shparlinski, Igor E., and Kam Hung Yau. "Double exponential sums with exponential functions." International Journal of Number Theory 13, no. 10 (October 16, 2017): 2531–43. http://dx.doi.org/10.1142/s179304211750141x.

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We obtain several estimates for double rational exponential sums modulo a prime [Formula: see text] with products [Formula: see text] where both [Formula: see text] and [Formula: see text] run through short intervals and [Formula: see text] is fixed integer. We also obtain some new estimates for the number of points on exponential modular curves [Formula: see text] and similar.
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Proskurin, N. V. "On Cubic Exponential Sums and Gauss Sums." Journal of Mathematical Sciences 234, no. 5 (September 10, 2018): 697–700. http://dx.doi.org/10.1007/s10958-018-4037-0.

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Cochrane, Todd, Christopher Pinner, and Jason Rosenhouse. "Sparse polynomial exponential sums." Acta Arithmetica 108, no. 1 (2003): 37–52. http://dx.doi.org/10.4064/aa108-1-4.

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Štefaňák, M., D. Haase, W. Merkel, M. S. Zubairy, and W. P. Schleich. "Factorization with exponential sums." Journal of Physics A: Mathematical and Theoretical 41, no. 30 (July 15, 2008): 304024. http://dx.doi.org/10.1088/1751-8113/41/30/304024.

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Erdélyi, T. "Inequalities for exponential sums." Sbornik: Mathematics 208, no. 3 (March 31, 2017): 433–64. http://dx.doi.org/10.1070/sm8670.

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Fouvry, Etienne, and Henryk Iwaniec. "Exponential sums with monomials." Journal of Number Theory 33, no. 3 (November 1989): 311–33. http://dx.doi.org/10.1016/0022-314x(89)90067-x.

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Adolphson, Alan, and Steven Sperber. "On twisted exponential sums." Mathematische Annalen 290, no. 1 (March 1991): 713–26. http://dx.doi.org/10.1007/bf01459269.

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Dissertations / Theses on the topic "Exponential sums"

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Louvel, Benoît. "Twisted Kloosterman sums and cubic exponential sums." Doctoral thesis, Montpellier 2, 2008. http://hdl.handle.net/11858/00-1735-0000-0006-B3CB-A.

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Chambille, Saskia. "Exponential sums, cell decomposition and p-adic integration." Thesis, Lille 1, 2018. http://www.theses.fr/2018LIL1I023/document.

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Dans cette thèse nous étudions des sommes exponentielles et des intégrales p-adiques, en utilisant la théorie des modèles et la géométrie. La première partie traite des sommes exponentielles dans des corps P-minimaux. La deuxième partie examine le comportement asymptotique des sommes exponentielles sur les corps p-adiques. Dans la première partie nous commençons par démontrer une théorème de décomposition cellulaire pour tous les corps P-minimaux, c.-à-d. indépendamment de l’existence des fonctions de Skolem définissables. En l’absence de ces fonctions nous introduisons les cellules en grappe régulières, inspirés par la notion classique de cellule p-adique de Denef. Notre décomposition cellulaire utilise les cellules classiques et les cellules en grappe régulières. Ensuite nous étendons la notion de fonction constructible exponentielle des structures semi-algébriques et sous-analytiques à tous les corps P-minimaux. Pour cela nous ajoutons des sommes exponentielles aux algèbres des fonctions constructibles. En utilisant notre décomposition cellulaire, nous démontrons que les fonctions constructibles exponentielles sont stables dans le contexte d’intégration. Cela signifie que l’intégration d’une fonction constructible exponentielle sur certaines de ses variables produit une fonction constructible exponentielle dans les autres variables. Dans la deuxième partie nous démontrons les conjectures d’Igusa, Denef-Sperber et Cluckers-Veys sur le comportement asymptotique des sommes exponentielles pour les polynômes dont le seuil log-canonique ne dépasse pas un demi. Nous apportons deux démonstrations ; l’une utilise l’intégration motivique et l’autre les fonctions zêtas d’Igusa
In this thesis we study p-adic exponential sums and integrals using ideas from model theory and geometry. The first part of this thesis deals with exponential sums in P-minimal fields. The second part discusses estimates for the asymptotic behaviour of exponential sums over p-adic fields. Our work on P-minimal fields starts with the proof of a cell decomposition theorem that holds in all P-minimal fields, i.e., independently of the existence of definable Skolem functions. For P-minimal fields that lack these functions, we introduce the notion of regular clustered cells. This notion is close to the classical notion of p-adic cells, that was introduced by Denef. Our cell decomposition uses both classical cells and regular clustered cells. Next, we extend the notion of exponential-constructible functions, already defined in the semi-algebraic and subanalytic setting, to all P-minimal fields. We do this by enlarging the algebras of constructible functions with exponential sums. Using our cell decomposition theorem we prove that exponential-constructible functions are stable under integration. This means that the act of integrating an exponential-constructible function over some of its variables produces an exponential-constructible function in the other variables. In our work on estimates for the asymptotic behaviour of exponential sums we prove the Igusa, Denef-Sperber and Cluckers-Veys conjectures for polynomials with log-canonical threshold at most one half. We give two different proofs, one using motivic integration, and the other one using the Igusa zeta functions
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Watt, N. "some problems in analytic number theory." Thesis, Bucks New University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384667.

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Alsulmi, Badria. "Generalized Jacobi sums modulo prime powers." Diss., Kansas State University, 2016. http://hdl.handle.net/2097/32668.

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Allison, Gisele. "Some problems related to incomplete character sums." Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285601.

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Chênevert, Gabriel. "Exponential sums, hypersurfaces with many symmetries and Galois representations." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=32386.

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The main theme of this thesis is the study of compatible systems of $\ell$-adic Galois representations provided by the étale cohomology of arithmetic varieties with a large group of symmetries. A canonical decomposition of these systems into isotypic components is proven (Section 3.1). The isotypic components are realized as the cohomology of the quotient with values in a certain sheaf, thus providing a geometrical interpretation for the rationality of the corresponding $L$-functions. A particular family of singular hypersurfaces $W_\ell^{m,n}$ of degree $\ell$ and dimension $m + n - 3$, admitting an action by a product of symmetric groups $S_m \times S_n$, arises naturally when considering the average moments of certain exponential sums (Chapter 4); asymptotics for these moments are obtained by relating them to the trace of the Frobenius morphism on the cohomology of the desingularization of the corresponding varieties, following the approach of Livné. Two other closely related classes of smooth hypersurfaces admitting an $S_n$-action are introduced in Chapter 3, and the character of the representation of the symmetric group on their primitive cohomology is computed. In particular, a certain smooth cubic hypersurface of dimension 4 is shown to carry a compatible system of 2-dimensional Galois representations. A variant of the Faltings-Serre method is developed in Chapter 5 in order to explicitly determine the corresponding modular form, whose existence is predicted by Serre's conjecture. We provide a systematic treatment of the Faltings-Serre method in a form amenable to generalization to Galois representations of other fields and to other groups besides $\GL_2$.
Le thème principal de cette thèse est l'étude des systèmes compatibles de représentations galoisiennes $\ell$-adiques provenant de la cohomologie étale de variétés arithmétiques admettant beaucoup de symétries. Une décomposition canonique de ces systèmes en composantes isotypiques est obtenue (section 3.1). Les composantes isotypiques sont décrites comme la cohomologie du quotient à valeurs dans un certain faisceau, fournissant ainsi une interprétation géométrique de la rationalité des fonctions $L$ correspondantes. Une famille spécifique d'hypersurfaces $W_\ell^{m,n}$ de degré $\ell$ et dimension $m+n-3$, admettant une action du produit de groupes symétriques $S_m \times S_n$, apparaît naturellement en lien avec les moments moyens de certaines sommes exponentielles (chapitre 4); le comportement limite de ces moments est obtenu en considérant la trace du morphisme de Frobenius sur la cohomologie de la désingularisation des variétés correspondantes, suivant l'approche développée par Livné. Deux autres classes apparentées d'hypersurfaces lisses admettant une action du groupe symétrique sont introduites au chapitre 3, et le caractère de la représentation de $S_n$ sur leur cohomologie primitive est calculé. En particulier, dans le cas d'une certaine hypersurface cubique de dimension 4, un système compatible de représentations galoisiennes de dimension 2 est obtenu. Une variante de la méthode de Faltings-Serre est développée dans le chapitre 5 afin de déterminer explicitement la forme modulaire correspondante, dont l'existence est prédite par la conjecture de Serre. Nous proposons un traitement systématique de la méthode de Falting
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Pigno, Vincent. "Prime power exponential and character sums with explicit evaluations." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/18277.

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Doctor of Philosophy
Department of Mathematics
Christopher Pinner
Exponential and character sums occur frequently in number theory. In most applications one is only interested in estimating such sums. Explicit evaluations of such sums are rare. In this thesis we succeed in evaluating three types of sums when p is a prime and m is sufficiently large. The twisted monomial sum, the binomial character sum, and the generalized Jacobi sum. We additionally show that these are all sums which can be expressed in terms of classical Gauss sums.
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Qin, Huan. "Averages of fractional exponential sums weighted by Maass forms." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5607.

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The purpose of this study is to investigate the oscillatory behavior of the fractional exponential sum weighted by certain automorphic forms for GL(2) x GL(3) case. Automorphic forms are complex-values functions defined on some topological groups which satisfy a number of applicable properties. One nice property that all automorphic forms admit is the existence of Fourier series expansions, which allows us to study the properties of automorphic forms by investigating their corresponding Fourier coefficients. The Maass forms is one family of the classical automorphic forms, which is the major focus of this study. Let f be a fixed Maass form for SL(3, Z) with Fourier coefficients Af(m, n). Also, let {gj} be an orthonormal basis of the space of the Maass cusp form for SL(2, Z) with corresponding Laplacian eigenvalues 1/4+kj^2, kj>0. For real α be nonzero and β>0, we considered the asymptotics for the sum in the following form Sx(f x gj, α, β) = ∑Af(m, n)λgj(n)e(αn^β)φ(n/X) where φ is a smooth function with compactly support, λgj(n) denotes the nth Fourier coefficient of gj, and X is a real parameter that tends to infinity. Also, e(x) = exp(2πix) throughout this thesis. We proved a bound of the weighted average sum of Sx(f x gj, α, β) over all Laplacian eigenvalues, which is better than the trivial bound obtained by the classical Rankin-Selberg method. In this case, we allowed the form varies so that we can obtain information about their oscillatory behaviors in a different aspect. Similar to the proofs of the subconvexity bounds for Rankin-Selberg L-functions for GL(2) x GL(3) case, the method we used in this study includes several sophisticated techniques such as weighted first and second derivative test, Kuznetsov trace formula, and Voronoi summation formula.
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Wong, Chi-Yan, and 黃志仁. "Some results on the error terms in certain exponential sums involving the divisor function." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B42577147.

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Wong, Chi-Yan. "Some results on the error terms in certain exponential sums involving the divisor function." Click to view the E-thesis via HKUTO, 2002. http://sunzi.lib.hku.hk/hkuto/record/B42577147.

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Books on the topic "Exponential sums"

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Korobov, N. M. Exponential sums and their applications. Dordrecht: Kluwer Academic Publishers, 1992.

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Graham, S. W. Van der Corputʼs method of exponential sums. Cambridge: Cambridge University Press, 1991.

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Koni͡agin, S. V. Character sums with exponential functions and their applications. Cambridge: Cambridge University Press, 1999.

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Exponential sums and differential equations. Princeton, N.J: Princeton University Press, 1990.

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Korobov, N. M. Exponential Sums and their Applications. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8032-8.

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Huxley, M. N. Area, lattice points, and exponential sums. Oxford: Clarendon Press, 1996.

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Graham, Sidney W. Van der Corput's method of exponential sums. Cambridge: Cambridge University Press, 1991.

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Graham, Sidney W. Van der Corput's method of exponential sums. Cambridge [England]: Cambridge University Press, 1991.

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Bachman, Gennady. On the coefficients of cyclotomic polynomials. Providence, R.I: American Mathematical Society, 1993.

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Shestopaloff, Yuri K. Sums of exponential functions and their new fundamental properties, with applications to natural phenomena. Toronto: AKVY Press, 2008.

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Book chapters on the topic "Exponential sums"

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Bordellès, Olivier. "Exponential Sums." In Universitext, 411–515. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54946-6_6.

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Bordellès, Olivier. "Exponential Sums." In Universitext, 297–353. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4096-2_6.

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Shparlinski, Igor. "Exponential Sums." In Cryptographic Applications of Analytic Number Theory, 37–60. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8037-4_4.

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Yuan, Wang. "Complete Exponential Sums." In Diophantine Equations and Inequalities in Algebraic Number Fields, 14–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58171-7_2.

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Korobov, N. M. "Complete Exponential Sums." In Exponential Sums and their Applications, 1–67. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8032-8_1.

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Korobov, N. M. "Weyl’s Sums." In Exponential Sums and their Applications, 68–138. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8032-8_2.

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Braess, Dietrich. "Approximation by Exponential Sums." In Nonlinear Approximation Theory, 168–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-61609-9_6.

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Daboussi, H. "On some Exponential Sums." In Analytic Number Theory, 111–18. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4612-3464-7_9.

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Ramaré, Olivier. "Three Arithmetical Exponential Sums." In Excursions in Multiplicative Number Theory, 259–74. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-73169-4_26.

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Cai, Jin-Yi, Xi Chen, Richard Lipton, and Pinyan Lu. "On Tractable Exponential Sums." In Frontiers in Algorithmics, 148–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14553-7_16.

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Conference papers on the topic "Exponential sums"

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Okada, Tatsuya, Zenji Kobayashi, Takeshi Sekiguchi, Yasunobu Shiota, and Takao Komatsu. "On exponential sums of digital sums related to Gelfond's theorem." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841904.

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Diederichs, Benedikt, and Armin Iske. "Parameter estimation for bivariate exponential sums." In 2015 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2015. http://dx.doi.org/10.1109/sampta.2015.7148940.

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SHPARLINSKI, IGOR E. "OPEN PROBLEMS ON EXPONENTIAL AND CHARACTER SUMS." In Proceedings of the 5th China-Japan Seminar. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814289924_0010.

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Schmidt, Kai-Uwe. "ℤ4-valued quadratic forms and exponential sums." In 2008 IEEE International Symposium on Information Theory - ISIT. IEEE, 2008. http://dx.doi.org/10.1109/isit.2008.4595495.

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Štefaňák, M., W. Merkel, M. Mehring, and W. P. Schleich. "NMR implementation of exponential sums for integer factorization." In Proceedings of the International Symposium. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812818942_0006.

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Moore, Cristopher, and Leonard J. Schulman. "Tree codes and a conjecture on exponential sums." In ITCS'14: Innovations in Theoretical Computer Science. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2554797.2554813.

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Barvinok, Alexander I. "Computing the volume, counting integral points, and exponential sums." In the eighth annual symposium. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/142675.142713.

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Hai Xin and Li Chao. "Value distributions of exponential sums from perfect nonlinear functions." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5623154.

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Helleseth, Tor. "Cross-correlation of M-sequences, exponential sums and dickson polynomials." In 2009 Fourth International Workshop on Signal Design and its Applications in Communications (IWSDA). IEEE, 2009. http://dx.doi.org/10.1109/iwsda.2009.5346425.

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Tonn, David, and Bourama Toni. "Expansion in Exponential Sums with Application to Discrete Complex Image Theory." In 2022 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/USNC-URSI). IEEE, 2022. http://dx.doi.org/10.1109/ap-s/usnc-ursi47032.2022.9886135.

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