Results 11 to 20 of about 2,774 (214)

A mean value estimate for real character sums [PDF]

Acta Arithmetica, 1995
Let \(S(Q)\) be the set of all primitive real characters of conductor at most \(Q\), and let \(n\) run over square-free numbers. It is shown that \[ \sum_{\chi \in S(Q)} \Bigl |\sum_{n \leq N} a_n \chi (n) \Bigr |^2 \ll (QN)^\varepsilon (Q + N) \sum_{n \leq N} |a_n |^2, \] for any \(\varepsilon > 0\). This sharpens an estimate of \textit{P. D. T.
D. R. Heath‐Brown
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Upper bound estimate of character sums over Lehmer’s numbers [PDF]

Journal of Inequalities and Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, Di, Zhang, Wenpeng
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Some estimate of character sums and its applications [PDF]

Journal of Inequalities and Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Jianghua, Han, Di
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One kind hybrid character sums and their upper bound estimates [PDF]

Journal of Inequalities and Applications, 2018
The main purpose of this paper is applying the analysis method, the properties of Lucas polynomials and Gauss sums to study the estimation problems of some kind hybrid character sums. In the end, we obtain several sharp upper bound estimates for them. As some applications, we prove some new and interesting combinatorial identities.
Jianhong Zhao, Xiao Wang
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$p$-adic estimates for multiplicative character sums [PDF]

, 2011
9 ...
Adolphson, Alan, Sperber, Steven
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Estimating Additive Character Sums for Fuchsian Groups [PDF]

The Ramanujan Journal, 2003
Some forty years ago, in connection with the (Eichler) cohomology of automorphic forms, \textit{M. Eichler} [Acta Arith. 11, 169--180 (1965; Zbl 0148.32503)] introduced (what later came to be called) the ``generalized Poincaré (in particular, Eistenstein) series''.
Goldfeld, Dorian, O'Sullivan, Cormac
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Estimates for Nonsingular Mixed Character Sums [PDF]

International Mathematics Research Notices, 2010
a nontrivial multiplicative character of k. We extend χ to k by defining χ(0) = 0. We wish to consider character sums over An, n ≥ 1, of the following form. We are given a polynomial f (x) := f (x1, . . . , xn) in k[x1, . . . ,Xn] of degree d ≥ 1, and we are given a second polynomial g(X) := g(x1, . . . , xn) in k[x1, . . . , xn] of degree e ≥ 1.
Nicholas M. Katz
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Estimates for Character Sums in Finite Fields of Order p2 and p3 [PDF]

Proceedings of the Steklov Institute of Mathematics, 2018
Let $p$ be a prime number, $\mathbb{F}_{p^n}$ be the finite field of order $p^n$, and $\{ω_1,\ldotsω_n\}$ be a basis of $\mathbb{F}_{p^n}$ over $\mathbb{F}_p$. Let, further, $N_i,H_i$ be integers such that $1\leq H_i\leq p$, $\,\,i=1,\ldots,n$. Define $n$-dimensional parallelepiped $B\subseteq\mathbb{F}_{p^n}$ as follows: $$B=\left\{\sum_{i=1}^nx_iω_i \
Mikhail R. Gabdullin
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Estimates for short character sums evaluated at homogeneous polynomials [PDF]

Journal of the London Mathematical Society
Abstract Let be a prime. We prove bounds on short Dirichlet character sums evaluated at a class of homogeneous polynomials in arbitrary dimensions. In every dimension, this bound is nontrivial for sums over boxes with side lengths as short as for any . Our methods capitalize on the relationship between characters mod and characters
Rena Chu
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Burgess‐type character sum estimates over generalized arithmetic progressions of rank 2 [PDF]

Bulletin of the London Mathematical Society
Abstract We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank 2 in prime fields . The core of our proof is a sharp upper bound for the multiplicative energy of these sets, established by adapting an argument of Konyagin and leveraging tools from the geometry of ...
Ali Alsetri, Xuancheng Shao
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