Results 11 to 20 of about 8,685 (113)

Riemann Hypothesis and Random Walks: the Zeta case

, 2017
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 $\
LeClair, André
core   +1 more source

Rudnick and Soundararajan's Theorem for Function Fields

, 2015
In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet $L$-functions.
Andrade, Julio
core   +1 more source

High pseudomoments of the Riemann zeta function [PDF]

, 2018
The pseudomoments of the Riemann zeta function, denoted $\mathcal{M}_k(N)$, are defined as the $2k$th integral moments of the $N$th partial sum of $\zeta(s)$ on the critical line.
Brevig, Ole Fredrik, Heap, Winston
core   +2 more sources

Integral Transforms in Number Theory

Axioms
Integral 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, Takako Kuzumaki, Shigeru Kanemitsu   +2 more
doaj   +1 more source

A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards

, 2012
We have obtained an explicit expression for the spectral zeta functions and for the heat kernel of strings, drums and quantum billiards working to third order in perturbation theory, using a generalization of the binomial theorem to operators.
Arendt W., Avellaneda M., Bender C. M., Elizalde E., Kirsten K., Paolo Amore   +5 more
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Spectral Zeta Functions for a Cylinder and a Circle

, 2002
Spectral zeta functions $\zeta(s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s
Nesterenko, V. V., Pirozhenko, I. G.
core   +1 more source

Impact of Uncertain Parameters on Navier–Stokes Equations With Heat Transfer via Polynomial Chaos Expansion

International Journal for Numerical Methods in Fluids, EarlyView.
This study investigates the impact of uncertain parameters on Navier–Stokes equations coupled with heat transfer using the Intrusive Polynomial Chaos Method (IPCM). Sensitivity equations are formulated for key input parameters, such as viscosity and thermal diffusivity, and solved numerically using the Finite Element‐Volume method.
N. Nouaime, B. Després, M. A. Puscas, C. Fiorini   +3 more
wiley   +1 more source

Rational points in a family of conics over F2(t)$\mathbb {F}_2(t)$

Mathematische Nachrichten, EarlyView.
Abstract Serre famously showed that almost all plane conics over Q$\mathbb {Q}$ have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over F2(t)$\mathbb {F}_2(t)$ which illustrates new behavior.
Daniel Loughran, Judith Ortmann
wiley   +1 more source

Approximation of Dirac operators with δ‐shell potentials in the norm resolvent sense, II: Quantitative results

Mathematische Nachrichten, EarlyView.
Abstract This paper is devoted to the approximation of two‐ and three‐dimensional Dirac operators HV∼δΣ$H_{\widetilde{V} \delta _\Sigma }$ with combinations of electrostatic and Lorentz scalar δ$\delta$‐shell interactions in the norm resolvent sense. Relying on results from Behrndt, Holzmann, and Stelzer‐Landauer [Math. Nachr.
Jussi Behrndt, Markus Holzmann, Christian Stelzer‐Landauer   +2 more
wiley   +1 more source

Generalized Riemann hypotheses: sufficient and equivalent criteria [PDF]

, 2010
This paper presents new sufficient and equivalent conditions for the generalized version of the Riemann Hypothesis. The paper derives also statements and remarks concerning zero-free regions, modified Hadamard-product formulas and the behaviour of ...
Schipani, Davide
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