Results 11 to 20 of about 2,094 (162)

A Tapestry of Ideas with Ramanujan’s Formula Woven In

Axioms
Zeta-functions play a fundamental role in many fields where there is a norm or a means to measure distance. They are usually given in the forms of Dirichlet series (additive), and they sometimes possess the Euler product (multiplicative) when the domain ...
Nianliang Wang, Takako Kuzumaki, Shigeru Kanemitsu   +2 more
doaj   +2 more sources

Fourier Interpolation with Zeros of Zeta and L-Functions [PDF]

, 2022
We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other L-functions.
Bondarenko, Andrii, Seip, Kristian, Radchenko, Danylo   +2 more
core   +3 more sources

On the Mishou Theorem for Zeta-Functions with Periodic Coefficients

Mathematics, 2023
Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dirichlet ...
A. Balčiūnas, M. Jasas, R. Macaitienė, D. Šiaučiūnas   +3 more
semanticscholar   +1 more source

Unified Theory of Zeta-Functions Allied to Epstein Zeta-Functions and Associated with Maass Forms

Mathematics, 2023
In this paper, we shall establish a hierarchy of functional equations (as a G-function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional ...
Nianliang Wang, T. Kuzumaki, S. Kanemitsu   +2 more
semanticscholar   +1 more source

Discrete Universality of absolutely convergent Dirichlet Series

Mathematical Modelling and Analysis, 2022
In the paper, an universality theorem of discrete type on the approximation of analytic functions by shifts of a special absolutely convergent Dirichlet series is obtained.
M. Jasas, A. Laurinčikas, M. Stoncelis, D. Šiaučiūnas   +3 more
semanticscholar   +1 more source

Probabilistic Aspects of Dirichlet Series [PDF]

, 2011
We investigate and generalise some properties of a family of probability distributions closely related to the Riemann zeta function. Random variables that have the property that divisibility by a set of distinct primes occurs as a set of independent ...
Lyons, Simon
core   +1 more source

Boundary Properties of Modified Zeta Functions and Function Spaces of Dirichlet Series [PDF]

, 2009
Ordinary Dirichlet series, of which the Riemann zeta function is the most important, play a prominent role in classical analysis and number theory, and in modern mathematics.
Olsen, Jan-Fredrik
core   +1 more source

A Product Identity For Dirichlet Series Satisfying Hecke's Functional Equation [PDF]

Hacettepe Journal of Mathematics and Statistics
In this paper, we give an analogue of Wilton's product formula for Dirichlet series that satisfy Hecke's functional equation. We apply our results to obtain identities for Hecke series, L-functions associated to modular forms, Epstein zeta functions ...
Efe Gürel
semanticscholar   +1 more source

GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS [PDF]

, 2002
This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers ...
Sándor, József
core   +1 more source

Riemann Hypothesis and Random Walks: The Zeta Case

, 2021
In previous work, it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its L-function is valid to the right of the critical line ℜ ...
André LeClair
core   +1 more source