Results 11 to 20 of about 1,483,300 (312)
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020 We obtain new bounds of exponential sums modulo a prime $p$ with binomials $ax^k + bx^n$. In particular, for $k=1$, we improve the bound of Karatsuba (1967) from $O(n^{1/4} p^{3/4})$ to $O\left(p^{3/4} + n^{1/3}p^{2/3}\right)$ for any $n$, and then use it to improve the bound of Akulinichev (1965) from $O(p^{5/6})$ to $O(p^{4/5})$ for $n | (p-1)$.
Shparlinski, Igor, Voloch, Felipe
openaire +4 more sources
A new fourth power mean of two-term exponential sums
Open Mathematics, 2019 The main purpose of this paper is to use analytic methods and properties of quartic Gauss sums to study a special fourth power mean of a two-term exponential sums modp, with p an odd prime, and prove interesting new identities.
Li Chen, Xiao Wang
doaj +2 more sources
Exponential sums equations and tropical geometry [PDF]
Selecta Mathematica, 2022 Zilber’s Exponential-Algebraic Closedness Conjecture states that algebraic varieties in $${{\mathbb {C}}}^n \times ({{\mathbb {C}}}^\times )^n$$ C n × ( C × ) n intersect the graph of complex exponentiation, unless that contradicts the algebraic and ...
F. Gallinaro
semanticscholar +1 more source
Exact Reconstruction of Extended Exponential Sums using Rational Approximation of their Fourier Coefficients [PDF]
Analysis and Applications, 2021 In this paper, we derive a new recovery procedure for the reconstruction of extended exponential sums of the form [Formula: see text], where the frequency parameters [Formula: see text] are pairwise distinct.
Nadiia Derevianko, G. Plonka-Hoch
semanticscholar +1 more source
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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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
semanticscholar +2 more sources
Multilinear exponential sums with a general class of weights [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2019 In this paper we obtain some new estimates for multilinear exponential sums in prime fields with a more general class of weights than previously considered.
Bryce Kerr, Simon Macourt
semanticscholar +1 more source
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
semanticscholar +1 more source
IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES [PDF]
Forum of Mathematics, Pi, 2018 We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of ...
R. Cluckers, M. Mustaţă, K. Nguyen
semanticscholar +1 more source