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A hybrid mean value related to certain Hardy sums and Kloosterman sums

Xiaoyan Guo, Wenpeng Zhang (2011)

Czechoslovak Mathematical Journal

The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.

À la recherche de petites sommes d'exponentielles

Étienne Fouvry, Philippe Michel (2002)

Annales de l’institut Fourier

Soit f ( x ) une fraction rationnelle à coefficients entiers, vérifiant des hypothèses assez générales. On prouve l’existence d’une infinité d’entiers n , ayant exactement deux facteurs premiers, tels que la somme d’exponentielles x = 1 n exp ( 2 π i f ( x ) / n ) soit en O ( n 1 2 - β f ) , où β f > 0 est une constante ne dépendant que de la géométrie de f . On donne aussi des résultats de répartition du type Sato-Tate, pour certaines sommes de Salié, modulo n , avec n entier comme ci- dessus.

A note on signs of Kloosterman sums

Kaisa Matomäki (2011)

Bulletin de la Société Mathématique de France

We prove that the sign of Kloosterman sums Kl ( 1 , 1 ; n ) changes infinitely often as n runs through the square-free numbers with at most 15 prime factors. This improves on a previous result by Sivak-Fischler who obtained 18 instead of 15. Our improvement comes from introducing an elementary inequality which gives lower and upper bounds for the dot product of two sequences whose individual distributions are known.

A purely analytical lower bound for L ( 1 , χ )

Olivier Ramaré (2009)

Annales mathématiques Blaise Pascal

We give a simple proof of L ( 1 , χ ) q 2 ω ( q ) when χ is an odd primitiv quadratic Dirichlet character of conductor q . In particular we do not use the Dirichlet class-number formula.

An identity involving Dedekind sums and generalized Kloosterman sums

Le Huan, Jingzhe Wang, Tingting Wang (2012)

Czechoslovak Mathematical Journal

The various properties of classical Dedekind sums S ( h , q ) have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums K ( m , n , r ; q ) . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of...

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