Results 11 to 20 of about 122,337 (231)
Generalised divisor sums of binary forms over number fields [PDF]
, 2016 Estimating averages of Dirichlet convolutions $1 \ast \chi$, for some real Dirichlet character $\chi$ of fixed modulus, over the sparse set of values of binary forms defined over $\mathbb{Z}$ has been the focus of extensive investigations in recent years,
Frei, Christopher, Sofos, Efthymios
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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_ ...
openaire +2 more sources
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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Double Character Sums over Subgroups and Intervals [PDF]
, 2014 We estimate double sums $$ S_\chi(a, I, G) = \sum_{x \in I} \sum_{\lambda \in G} \chi(x + a\lambda), \qquad 1\le a < p-1, $$ with a multiplicative character $\chi$ modulo $p$ where $I= \{1,\ldots, H\}$ and $G$ is a subgroup of order $T$ of the ...
Bourgain +7 more
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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.
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The distribution of the maximum of character sums
, 2012 We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character sums normalized by the square root of the modulus ...
Granville +2 more
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Character sums to smooth moduli are small
, 2007 Recently, Granville and Soundararajan have made fundamental breakthroughs in the study of character sums. Building on their work and using estimates on short character sums developed by Graham-Ringrose and Iwaniec, we improve the Polya-Vinogradov ...
Davenport +12 more
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One level density of low-lying zeros of families of $L$-functions [PDF]
, 2010 In this paper, we prove some one level density results for low-lying zeros of families of $L$-functions. More specifically, the families under consideration are that of $L$-functions of holomorphic Hecke eigenforms of level 1 and weight $k$ twisted with ...
Davenport +4 more
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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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Counting Smooth Solutions to the Equation A+B=C [PDF]
, 2011 This paper studies integer solutions to the Diophantine equation A+B=C in which none of A, B, C have a large prime factor. We set H(A, B,C) = max(|A|, |B|, |C|), and consider primitive solutions (gcd}(A, B, C)=1) having no prime factor p larger than (log
Lagarias, J. C., Soundararajan, K.
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