scholarly journals Some $\Omega$-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem

1997 ◽  
Vol 9 (1) ◽  
pp. 41-50
Author(s):  
Jerzy Kaczorowski ◽  
Bogdan Szydło
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Divisor Problem ◽  
Fourth Power ◽  
Power Moment ◽  
The Riemann Zeta Function ◽  
Additive Divisor Problem ◽  
Riemann Zeta ◽  
Additive Divisor

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 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 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.

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