Results 21 to 30 of about 1,424,186 (337)
Restriction of Exponential Sums to Hypersurfaces [PDF]
International mathematics research notices, 2021 We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale parameter $N$, apart from
C. Demeter, B. Langowski
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On families of additive exponential sums
Finite Fields and Their Applications, 2005 AbstractIn this paper we compute geometric monodromy groups of additive exponential sums over BbbAn. Our approach builds on work of N. Katz, and involves p-adic analysis of explicit sums and computation of the Galois group of an equation over a function field in characteristic 2.
Šuch, Ondrej
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A BESSEL DELTA METHOD AND EXPONENTIAL SUMS FOR GL(2) [PDF]
Quarterly Journal of Mathematics, 2019 In this paper, we introduce a simple Bessel $\delta $-method to the theory of exponential sums for $\textrm{GL}_2$. Some results of Jutila on exponential sums are generalized in a less technical manner to holomorphic newforms of arbitrary level and ...
Keshav Aggarwal +3 more
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A new kth derivative estimate for exponential sums via Vinogradov’s mean value [PDF]
Proceedings of the Steklov Institute of Mathematics, 2017 We give a slight refinement to the process by which estimates for exponential sums are extracted from bounds for Vinogradov’s mean value. Coupling this with the recent works of Wooley, and of Bourgain, Demeter and Guth, providing optimal bounds for the ...
D. R. Heath-Brown
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p-adic estimates of exponential sums on curves [PDF]
Algebra & Number Theory, 2019 The purpose of this article is to prove a ``Newton over Hodge'' result for exponential sums on curves. Let $X$ be a smooth proper curve over a finite field $\mathbb{F}_q$of characteristic $p\geq 5$ and let $V \subset X$ be an affine curve.
Joe Kramer-Miller
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Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2018 We prove non-trivial bounds for bilinear forms with hyper-Kloosterman sums with characters modulo a prime $q$ which, for both variables of length $M$, are non-trivial as soon as $M\geq q^{3/8+\delta}$ for any $\delta>0$. This range, which matches Burgess'
E. Kowalski, P. Michel, W. Sawin
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ON THE DISTRIBUTION OF THE MAXIMUM OF CUBIC EXPONENTIAL SUMS [PDF]
Journal of the Institute of Mathematics of Jussieu, 2018 In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as ‘Birch sums’. Our main theorem gives upper and lower bounds (of nearly the same order of magnitude) for the distribution of
Youness Lamzouri
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From Oscillatory Integrals and Sublevel Sets to Polynomial Congruences and Character Sums [PDF]
, 2010 We present a slight extension of a classical lemma of Hensel and give various applications to polynomial congruences and character sums; in particular, we give a new proof of a classical result of Hua on complete exponential sums.
James Wright, Wright, James
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On the Hybrid Power Mean of Two-Term Exponential Sums and Cubic Gauss Sums
Journal of Mathematics, 2021 In this paper, an interesting third-order linear recurrence formula is presented by using elementary and analytic methods. This formula is concerned with the calculating problem of the hybrid power mean of a certain two-term exponential sums and the ...
Shaofan Cao, Tingting Wang
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Bounds for the Rate of Convergence in the Generalized Rényi Theorem
Mathematics, 2022 In the paper, an overview is presented of the results on the convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson random sums, including the case where the mixing law is itself a mixed ...
Victor Korolev
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