COMPLETE ASYMPTOTIC EXPANSIONS FOR THE TRANSFORMED LERCH ZETA-FUNCTIONS VIA THE LAPLACE-MELLIN AND RIEMANN-LIOUVILLE OPERATORS (PRE-ANNOUNCEMENT) (Problems and prospects in Analytic Number Theory) [PDF]
, 2021 This is a pre-announcement version of the forthcoming paper [Complete asymptotic expansions for the transformed Lerch zeta-functions via the LaplaceMellin and Riemann-Liouville operators, preprint.].
KATSURADA, MASANORI
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New Classes of Degenerate Unified Polynomials [PDF]
, 2022 In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations.
Daniel Bedoya +7 more
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On off-critical zeros of lattice energies in the neighborhood of the Riemann zeta function [PDF]
19 pages, 4 figuresThe Riemann zeta function $\zeta(s):= \sum_{n=1}^{\infty} 1/n^s$ can be interpreted as the energy per point of the lattice $\mathbb{Z}$, interacting pairwisely via the Riesz potential $1/r^s$.
Travěnec, Igor +2 more
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ASYMPTOTICS FOR HIGHER DERIVATIVES OF THE LERCH ZETA-FUNCTION: APPLICATIONS TO THE FORMULAE OF KUMMER, LERCH AND GAUSS (Analytic Number Theory and Related Topics) [PDF]
, 2019 Let s be a complex variables, z a complex parameter, and a and λ real parameters with a > 0, and write e(s) = e2πis. The Lerch zeta-function φ(s, a, λ) is defined by the Dirichlet series Σ∞ l=0 e(λl)(a + l)−s (Res > 1), and its meromorphic continuation ...
KATSURADA, MASANORI
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Analysis in Fractional Calculus and Asymptotics Related to Zeta Functions [PDF]
, 2018 This thesis presents results in two apparently disparate mathematical fields which can both be examined -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders.
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СМЕШАННАЯ СОВМЕСТНАЯ УНИВЕРСАЛЬНОСТЬ ДЛЯ L-ФУНКЦИЙ КЛАССА СЕЛЬБЕРГА И ПЕРИОДИЧЕСКИХ ДЗЕТА-ФУНКЦИЙ ГУРВИЦА [PDF]
, 2016 In 1975, a Russian mathematician S. M. Voronin discovered the universality property of the Riemann zeta-function ζ(s), s = σ+it. Roughly speaking, this means that analytic functions from a wide class can be approximated uniformly on compact subsets of ...
Р. Мацайтене +1 more
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A Generating Function Technique for Beatty Sequences and Other Step Sequences [PDF]
, 2002 Let g(x,n), with x∈R+, be a step function for each n. Assuming certain technical hypotheses, we give a constant α and function f such that ∑∞n=1:g(x,n) can be written in the form α ...
O'Bryant, Kevin
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Values of the polygamma functions at rational arguments [PDF]
, 2007 Gauss in 1812, in his celebrated memoir on the hypergeometric series, presented a remarkable formula for the psi (or digamma) function, psi(z), at rational arguments z, which can be expressed in terms of elementary functions.
Choi, Junesang, Cvijović, Đurđe
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Joint discrete universality for periodic zeta-functions [PDF]
, 2019 In the paper, joint universality theorems for periodic zeta functions with multiplicative coefficients and periodic Hurwitz zeta-functions are proved. The main theorem of [11] is extended, and two new joint universality theorems on the approximation of a
Laurinčikas, Antanas
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NEW DOCTORAL DEGREES Integral expressions for series of functions of hypergeometric and Bessel types [PDF]
, 2011 This thesis presents some new results on integral expressions for series of functions of hypergeometric and Bessel types. Also there are derived two--sided inequalities of some hypergeometric functions, which are related with their integral ...
Jankov, Dragana, Dragana Jankov
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