scholarly journals The multidimensional Dirichlet divisor problem and zero free regions for the Riemann zeta function

2000 ◽  
Vol 28 (0) ◽  
pp. 131-140 ◽  
Author(s):  
A. A. Karatsuba
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Divisor Problem ◽  
The Riemann Zeta Function ◽  
Dirichlet Divisor Problem ◽  
Riemann Zeta

scholarly journals On the mean square of the Riemann zeta function and the divisor problem

2008 ◽  
Vol 83 (97) ◽  
pp. 71-86
Author(s):  
Yifan Yang
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Integral Transforms ◽  
Divisor Problem ◽  
Mean Square ◽  
The Riemann Zeta Function ◽  
Dirichlet Divisor Problem ◽  
Error Terms ◽  
Riemann Zeta ◽  
The Mean

Let ?(T) and E(T) be the error terms in the classical Dirichlet divisor problem and in the asymptotic formula for the mean square of the Riemann zeta function in the critical strip, respectively. We show that ?(T) and E(T) are asymptotic integral transforms of each other. We then use this integral representation of ?(T) to give a new proof of a result of M. Jutila.

scholarly journals A quadratic divisor problem and moments of the Riemann zeta-function

2020 ◽  
Vol 22 (12) ◽  
pp. 3953-3980
Author(s):  
Sandro Bettin ◽  
Hung Bui ◽  
Xiannan Li ◽  
Maksym Radziwiłł
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Divisor Problem ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals The generalized divisor problem and the Riemann hypothesis

1991 ◽  
Vol 122 ◽  
pp. 149-159 ◽  
Author(s):  
Hideki Nakaya
Keyword(s):  
Zeta Function ◽  
Natural Number ◽  
Complex Number ◽  
Riemann Zeta Function ◽  
Multiplicative Function ◽  
Riemann Hypothesis ◽  
Divisor Problem ◽  
Divisor Function ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Let dz(n) be a multiplicative function defined bywhere s = σ + it, z is a. complex number, and ζ(s) is the Riemann zeta function. Here ζz(s) = exp(z log ζ(s)) and let log ζ(s) take real values for real s > 1. We note that if z is a natural number dz(n) coincides with the divisor function appearing in the Dirichlet-Piltz divisor problem, and d-1(n) with the Möbious function.

scholarly journals On some upper bounds for the zeta-function and the Dirichlet divisor problem

2016 ◽  
Vol 12 (08) ◽  
pp. 2231-2239
Author(s):  
Aleksandar Ivić
Keyword(s):  
Zeta Function ◽  
Error Term ◽  
Upper Bounds ◽  
Mean Value ◽  
Divisor Problem ◽  
Asymptotic Formulas ◽  
Number Of Divisors ◽  
The Riemann Zeta Function ◽  
Dirichlet Divisor Problem ◽  
Riemann Zeta

Let [Formula: see text] be the number of divisors of [Formula: see text], let [Formula: see text] denote the error term in the classical Dirichlet divisor problem, and let [Formula: see text] denote the Riemann zeta-function. Several upper bounds for integrals of the type [Formula: see text] are given. This complements the results of [A. Ivić and W. Zhai, On some mean value results for [Formula: see text] and a divisor problem II, Indag. Math. 26(5) (2015) 842–866], where asymptotic formulas for [Formula: see text] were established for the above integral.

Representations and evaluations of the error term in a certain divisor problem

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Jun Furuya ◽  
Makoto Minamide ◽  
Yoshio Tanigawa
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Error Term ◽  
Divisor Problem ◽  
Type Formula ◽  
The Riemann Zeta Function ◽  
Direct Corollary ◽  
Riemann Zeta ◽  
Derivatives Of

AbstractIn this paper, we shall derive representations of the Chowla-Walum type formula for the error term in a divisor problem related to the derivatives of the Riemann zeta-function. As a direct corollary of this formula, we shall consider estimations of this error term.

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