Results 21 to 30 of about 59 (55)

Estimates of convolutions of certain number‐theoretic error terms

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 1, Page 1-23, 2004., 2004
Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number‐theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the ...
Aleksandar Ivić
wiley   +1 more source

Consecutive evaluation of Euler sums

International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 9, Page 555-561, 2002., 2002
We describe a simple method for a consecutive evaluation of the Euler sums S(r, p), r = 1, 2, … in terms of zeta values.
Khristo N. Boyadzhiev
wiley   +1 more source

A quantum field theoretical representation of Euler‐Zagier sums

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 127-148, 2002., 2002
We establish a novel representation of arbitrary Euler‐Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders.
Uwe Müller, Christian Schubert
wiley   +1 more source

Evaluation of integrals with hypergeometric and logarithmic functions

Open Mathematics, 2018
We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions.
Sofo Anthony
doaj   +1 more source

Decompositions of the extended Selberg class functions

Open Mathematics
Let F(s)F\left(s) be a function from the extended Selberg class. We consider decompositions F(s)=f(h(s))F\left(s)=f\left(h\left(s)), where ff and hh are meromorphic functions.
Garunkštis Ramūnas, Panavas Tadas, Šimenas Raivydas   +2 more
doaj   +1 more source

Limit theorems for a class of unbounded observables with an application to ‘Sampling the Lindelöf hypothesis’ [PDF]

MSC classification: Primary: 37A50: Relations with probability theory and stochastic processes Secondary: 60F05: Central limit and other weak theorems 11M06: zeta(s) and L(s,chi)We prove the central limit theorem (CLT), the first-order Edgeworth ...
Schindler, TI, Fernando, K
core   +1 more source

A kind of identities related to Riemann zeta-function

Open Mathematics
The main purpose of this paper is to study a kind of identities related to Riemann zeta-function. We first construct a new sequence involving trigonometric function.
Chen Zhuoyu, Deng Changlin
doaj   +1 more source

Asymptotic second moment of Dirichlet L-functions along a thin coset

Forum of Mathematics, Sigma
We prove an asymptotic formula for the second moment of central values of Dirichlet L-functions restricted to a coset. More specifically, consider a coset of the subgroup of characters modulo d inside the full group of characters modulo q. Suppose that
Bradford Garcia, Matthew P. Young
doaj   +1 more source

On generalized shifts of the Mellin transform of the Riemann zeta-function

Open Mathematics
In this article, we consider the asymptotic behaviour of the modified Mellin transform Z(s){\mathcal{Z}}\left(s), s=σ+its=\sigma +it, of the Riemann zeta-function using weak convergence of probability measures in the space of analytic functions defined ...
Laurinčikas Antanas, Šiaučiūnas Darius   +1 more
doaj   +1 more source

On certain properties and expansions of zeta matrix function, digamma matrix function and polygamma matrix function

, 2020
We introduce the generalized zeta matrix function, digamma matrix function and polygamma matrix function. We obtain the regions of convergence of these matrix functions, some recurrence relations and their integral representations.
Sahai, Vivek, Dwivedi, Ravi
core