Character sums and exponential sums

1976 ◽  
pp. 38-91
Author(s):  
Wolfgang M. Schmidt
Keyword(s):  
Exponential Sums ◽  
Character Sums

scholarly journals Sommes friables d'exponentielles et applications

2015 ◽  
Vol 67 (3) ◽  
pp. 597-638 ◽  
Author(s):  
Sary Drappeau
Keyword(s):  
Asymptotic Formula ◽  
Saddle Point ◽  
Exponential Sums ◽  
Prime Factor ◽  
Character Sums ◽  
Contour Integration ◽  
Point Method ◽  
Saddle Point Method ◽  
Greatest Prime Factor

AbstractAn integer is said to be y–friable if its greatest prime factor is less than y. In this paper, we obtain estimates for exponential sums over y–friable numbers up to x which are non–trivial when y ≥ . As a consequence, we obtain an asymptotic formula for the number of y-friable solutions to the equation a + b = c which is valid unconditionally under the same assumption. We use a contour integration argument based on the saddle point method, as developped in the context of friable numbers by Hildebrand and Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers.

scholarly journals A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Liu Miaohua ◽  
Li Xiaoxue
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Character Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Hybrid Mean Value

The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula for it.

scholarly journals The hybrid power mean of some special character sums of polynomials and two-term exponential sums modulo $ p $

2021 ◽  
Vol 6 (10) ◽  
pp. 10989-11004
Author(s):  
Wenpeng Zhang ◽  
◽  
Jiafan Zhang ◽  
Keyword(s):  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Analytic Method ◽  
Power Mean ◽  
Hybrid Power ◽  
Special Character ◽  
Modulo P ◽  
Hybrid Power Mean

<abstract><p>We consider the calculation problem of one kind hybrid power mean involving the character sums of polynomials and two-term exponential sums modulo $ p $, an odd prime, and use the analytic method and the properties of classical Gauss sums to give some identities and asymptotic formulas for them.</p></abstract>

scholarly journals On the two-term exponential sums and character sums of polynomials

2019 ◽  
Vol 17 (1) ◽  
pp. 1239-1248
Author(s):  
Yuankui Ma ◽  
Wenpeng Zhang
Keyword(s):  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

Abstract The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character sums of polynomials and two-term exponential sums modulo p, an odd prime, and acquire several accurate asymptotic formulas for them.

Exponential sums, character sums, sieve methods and distribution of prime numbers

2017 ◽  
Author(s):  
◽  
Victor Zhenyu Guo
Keyword(s):  
Exponential Sums ◽  
Classical Problem ◽  
Prime Numbers ◽  
Character Sums ◽  
Sieve Methods ◽  
University Of Missouri ◽  
Small Constant ◽  
Beatty Sequences ◽  
Almost Primes ◽  
Quadratic Nonresidue

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This thesis is focus on the methods of exponential sums and sieve methods applying to distribution of primes numbers in several forms, such as Piatetski-Shapiro primes, Beatty sequences, almost primes and primes in arithmetic progression. In the end, we also think about the classical problem in Burgess bound. We begin by explaining the importance of the methods of exponential sums. Together with sieve methods, we investigate the Piatetski-Shapiro primes from almost primes and the intersection between Piatetski-Shapiro primes and Betty sequences. Above all, we study primes in several forms from a "thin" integer set. We also study the distribution of consecutive prime numbers from two Beatty sequences by an assumption of a well-known conjecture. Finally, we turn to the methods of character sums and the problem of the least quadratic nonresidue. We improve the best known bound by changing the arbitrary small constant into a reciprocal of an infinite function. Possible future work is also discussed in the thesis.

A NOTE ON SOME CHARACTER SUMS OVER FINITE FIELDS

2015 ◽  
Vol 92 (1) ◽  
pp. 32-43
Author(s):  
XIWANG CAO ◽  
GUANGKUI XU
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Boolean Functions ◽  
Exponential Sums ◽  
Character Sums ◽  
Walsh Spectrum

In this paper, we present a decomposition of the elements of a finite field and illustrate the efficiency of this decomposition in evaluating some specific exponential sums over finite fields. The results can be employed in determining the Walsh spectrum of some Boolean functions.

Large families of pseudorandom binary lattices by using the multiplicative inverse modulo P

2019 ◽  
Vol 15 (03) ◽  
pp. 527-546
Author(s):  
Huaning Liu
Keyword(s):  
Exponential Sums ◽  
Character Sums ◽  
Two Dimensional ◽  
Multiplicative Inverse ◽  
Avalanche Effect ◽  
One Dimensional ◽  
Modulo P ◽  
Large Families ◽  
Pseudorandom Measures

Hubert, Mauduit and Sárközy introduced pseudorandom measures for finite pseudorandom binary lattices. Gyarmati, Mauduit, Sárközy and Stewart presented some natural and flexible constructions, which are the two-dimensional extensions and modifications of a few one-dimensional constructions. The upper estimates for the pseudorandom measures of their binary lattices are based on the principle that character sums or exponential sums in two variables can be estimated by fixing one of the variables. In this paper, we constructed two large families of [Formula: see text] dimensional pseudorandom binary lattices by using the multiplicative inverse modulo [Formula: see text], and study the properties: pseudorandom measure, collision and avalanche effect.

scholarly journals The character sum of polynomials with k variables and two-term exponential sums

2021 ◽  
Vol 27 (1) ◽  
pp. 112-124
Author(s):  
Xiaoling Xu ◽  
◽  
Jiafan Zhang ◽  
Wenpeng Zhang ◽  
◽  
...  
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Character Sum ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

The main purpose of this paper is using the properties of the classical Gauss sums and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sums of polynomials with k variables and the two-term exponential sums, and give an identity and asymptotic formula for it.

Sign in / Sign up

Export Citation Format

Share Document