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
On certain properties and expansions of zeta matrix function, digamma matrix function and polygamma matrix function [PDF]
, 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
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
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
Decompositions of the extended Selberg class functions
Open MathematicsLet 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 +2 more
doaj +1 more source
The average order of the Dirichlet series of the gcd-sum function [PDF]
, 2007 Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the ...
Broughan, Kevin A.
core
A kind of identities related to Riemann zeta-function
Open MathematicsThe 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, SigmaWe 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
Orthogonal forms: a simple tool for proving the irartionality of $\zeta (3)$ [PDF]
, 2009 33 pages, no figures.-- MSC2000 codes: Primary 42C05, 11B37, 11J72, 11M06; Secondary 30B70, 11A55, 11J70, 33C47.Submitted to: Journal of Approximation TheoryA new proof of the irrationality of $\zeta(3)$ is given. The orthogonality relation among certain
Arvesú Carballo, Jorge, Arvesú, Jorge
core +1 more source
Twisted quadratic moments for Dirichlet L-functions at s = 2 [PDF]
, 2019 International audienceLet c, n be given positive integers. Let q > 2 be coprime with c. Let X q be the multiplicative group of order φ(q) of the Dirichlet characters modulo q. Set M (q, c, n) := 2 φ(q) χ∈Xq χ(−1)=(−1) n χ(c)|L(n, χ)| 2.
Louboutin, Stéphane
core +1 more source