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Estimates for character sums with various convolutions [PDF]

Acta Arithmetica, 2017
17 ...
Brandon Hanson
exaly   +5 more sources

Estimates for Mixed Character Sums [PDF]

Geometric and Functional Analysis, 2008
We give sharp estimates for certain families of exponential sums in several variables over finite fields.
Katz Nicholas M
exaly   +3 more sources

Estimates for Character Sums [PDF]

Proceedings of the American Mathematical Society, 1993
We give a number of estimates for character sums \[ ∑
Friedlander, J., Iwaniec, H.
  +5 more sources

An estimate for character sums [PDF]

Journal of the American Mathematical Society, 1989
Let \(F\) be a finite field and \(E=F(x)\) an extension of degree \(n\). Let \(\chi\) be a nonprincipal character of \(E\). The author deduces from Weil's theorem that \[ S=| \sum_{t\in F}\chi (t-x)| \leq (n-1)\sqrt{\#F}, \] and a generalization of this inequality. This improves the estimate (for \(F\) a prime-field) \(S=0(\#F^{1-(n+1)})\) obtained by \
Nicholas M. Katz
  +5 more sources

Character sums estimates and an application to a problem of Balog [PDF]

Indiana University Mathematics Journal, 2022
We prove new bounds for sums of multiplicative characters over sums of set with small doubling and applying this result we break the square--root barrier in a problem of Balog concerning products of differences in a field of prime order.
Schoen, Tomasz, Shkredov, Ilya
  +5 more sources

A Chevalley-Warning approach to 𝑝-adic estimates of character sums [PDF]

Proceedings of the American Mathematical Society, 1995
The elementary Chevalley-Warning congruence method is applied to obtain several p -adic estimates of character sums over finite fields.
Da Qing Wan
  +5 more sources

A character-sum estimate and applications [PDF]

Acta Arithmetica, 1998
Let \(\chi\) be a non-principal Dirichlet character mod \(n\), and define \(S_N(H,\chi)=\sum_ ...
Karl K. Norton
openaire   +3 more sources

Estimates for trilinear and quadrilinear character sums [PDF]

Revista Matemática Iberoamericana
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between Farey fractions is given.
Étienne Fouvry, Igor E. Shparlinski, Ping Xi   +2 more
  +6 more sources

Estimates of character sums with exponential function [PDF]

Acta Arithmetica, 2001
Let \(n \geq 2\) and \(\lambda\) be integers satisfying \((n, \lambda)=1\) and \(\lambda\) belonging to the exponent \(d\) modulo \(n\). Given a primitive Dirichlet character \(\chi\) mod \(n\) the author proves the estimate \[ \left|\sum_{x=1}^X \chi(a \lambda^x +b) \right|< \sqrt{n} \left( \frac{2}{\pi} \log n + \frac{7}{5} \right).
Hong Yu
openaire   +2 more sources

Estimates for Character Sums and DirichletL-Functions to Smooth Moduli [PDF]

International Mathematics Research Notices, 2015
We use the $q$-analogue of van der Corput's method to estimate short character sums to smooth moduli. If $χ$ is a primitive Dirichlet character modulo a squarefree, $q^δ$-smooth integer $q$ we show that $$L(\frac12,χ)\ll_εq^{\frac{27}{164}+O(δ)+ε}.$$
A. J. Irving
  +6 more sources