Results 11 to 20 of about 169 (129)
Zeta-regularization of arithmetic sequences [PDF]
EPJ Web of Conferences, 2020 Is it possible to give a reasonable value to the infinite product 1 × 2 × 3 × · · · × n × · · · ? In other words, can we define some sort of convergence of the finite product 1 × 2 × 3 × · · · × n when n goes to infinity?
Allouche Jean-Paul
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A Tapestry of Ideas with Ramanujan’s Formula Woven In
AxiomsZeta-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 +2 more
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Integral Transforms in Number Theory
AxiomsIntegral transforms play a fundamental role in science and engineering. Above all, the Fourier transform is the most vital, which has some specifications—Laplace transform, Mellin transform, etc., with their inverse transforms. In this paper, we restrict
Guodong Liu +2 more
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Anisotropic Memristive Switching in NbOCl<sub>2</sub> Enabled by Directional Oxygen Ion Migration. [PDF]
Adv Sci (Weinh)This study investigates strongly orientation‐dependent memristive switching in anisotropic NbOCl2, observed exclusively along the in‐plane c‐axis. The switching originates from direction‐selective oxygen‐ion migration and vacancy propagation that modulate the Pd/NbOCl2 Schottky barrier, enabling short‐term plasticity.
Wang C +6 more
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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 +2 more
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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
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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
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Zeta functions of singular curves over finite fields [PDF]
, 1997 Let X be a complete, geometrically irreducible, algebraic curve defined over a finite field Fq and let (X ,t) be its zeta function [Ser1]. If X is a singular curve, two other zeta functions exist.
Zúñiga Galindo, Wilson Alvaro +1 more
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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
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Upper bounds for the density of universality. II [PDF]
, 2005 summary:We prove explicit upper bounds for the density of universality for Dirichlet series. This complements previous results [15]. Further, we discuss the same topic in the context of discrete universality.
Steuding, Jörn
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