scholarly journals On a hybrid mean value of the character sums over short intervals

2009 ◽  
Vol 41 (2) ◽  
pp. 113-128
Author(s):  
Zhefeng Xu ◽  
Wenpeng Zhang
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Short Intervals ◽  
Hybrid Mean Value

The hybrid mean value ofL-functions and a special character sums

2014 ◽  
Vol 37 (4) ◽  
pp. 563-570
Author(s):  
Jianghua Li ◽  
Xinqiang Qin ◽  
Fang Zhang
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Hybrid Mean Value ◽  
Special Character

scholarly journals A hybrid mean value of the inversion of L-functions and general quadratic Gauss sums

2002 ◽  
Vol 167 ◽  
pp. 1-15 ◽  
Author(s):  
Wenpeng Zhang ◽  
Yuping Deng
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Analytic Method ◽  
Power Mean ◽  
Hybrid Mean Value

AbstractThe main purpose of this paper is, using the estimates for character sums and the analytic method, to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums, and give two interesting asymptotic formulas.

scholarly journals Mean Value of the General Dedekind Sums over Interval \({[1,\frac{q}{p})}\)

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2079
Author(s):  
Lei Liu ◽  
Zhefeng Xu
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Dedekind Sums ◽  
Hybrid Mean Value ◽  
Asymptotic Formulae ◽  
The Mean

Let q>2 be a prime, p be a given prime with p<q. The main purpose of this paper is using transforms, the hybrid mean value of Dirichlet L-functions with character sums and the related properties of character sums to study the mean value of the general Dedekind sums over interval [1,qp), and give some interesting asymptotic formulae.

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.

WATT'S MEAN VALUE THEOREM AND CARMICHAEL NUMBERS

2008 ◽  
Vol 04 (02) ◽  
pp. 241-248 ◽  
Author(s):  
GLYN HARMAN
Keyword(s):  
Recent Work ◽  
Arithmetic Progression ◽  
Character Sums ◽  
Mean Value ◽  
Original Version ◽  
Mean Value Theorem ◽  
Carmichael Numbers ◽  
Short Intervals

It is shown that Watt's new mean value theorem on sums of character sums can be included in the method described in the author's recent work [6] to show that the number of Carmichael numbers up to x exceeds x⅓ for all large x. This is done by comparing the application of Watt's original version of his mean value theorem [8] to the problem of primes in short intervals [3] with the problem of finding "small" primes in an arithmetic progression.

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