Estimates for character sums
John B. Friedlander,Henryk Iwaniec +1 more
- Vol. 119, Iss: 2, pp 365-372
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In this article, a modified proof of the inequalities of P6lya-Vinogradov and of Burgess is presented, which displays the latter as a generalization of the former.Abstract:
We give a number of estimates for character sums Z EX(a+b) aE.V bER for rather general sets X, 7 . These give, in particular, a modified proof of the inequalities of P6lya-Vinogradov and of Burgess, which displays the latter as a generalization of the former.read more
Citations
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Sur certaines sommes d'exponentielles sur les nombres premiers
Étienne Fouvry,Philippe Michel +1 more
TL;DR: In this paper, des methodes de geometrie algebrique, nous donnons des majorations pour les sommes d'exponentielles de la forme suivante ∑ p≤x exp (2πi f(p) q ), ouq designe un nombre premier (grand), f(X) est une fraction rationnelle a coefficients entiers and p decrit les nombres premiers plus petits que x(≤ q).
Journal ArticleDOI
On a question of Davenport and Lewis and new character sum bounds in finite fields
TL;DR: In this paper, it was shown that χ is principal on a subfield F 2 of size pn/2, and χ ≥ 0 unless ϵ>0.
Journal ArticleDOI
Beurling primes with large oscillation
TL;DR: In this article, a Beurling generalized number system is constructed with integer counting function, whose prime counting function satisfies the oscillation estimate, and whose zeta function has infinitely many zeros on the curve σ=1−a/logt, t≥2, and no zero to the right of this curve, where a is chosen so that a>(4/e)(1−θ).
Journal ArticleDOI
Sumsets of reciprocals in prime fields and multilinear Kloosterman sums
Jean Bourgain,Moubariz Z. Garaev +1 more
TL;DR: In this article, the additive properties of the set of residue classes modulo a large prime were studied and new results on incomplete multilinear Kloosterman sums were obtained.
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On congruences with products of variables from short intervals and applications
TL;DR: In this paper, the authors obtained upper bounds on the number of solutions to congruences of the type (x ≥ 1 + s), where s is the cardinality of products of short intervals.
References
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Book
The Theory of the Riemann Zeta-Function
TL;DR: The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it one of the most important tools in the study of prime numbers as mentioned in this paper.