Results 101 to 110 of about 48,716 (213)

A new zero‐density estimate for ζ(s)$\zeta (s)$ and the error term in the prime number theorem

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract We will provide a new type of zero‐density estimate for ζ(s)$\zeta (s)$ when σ$\sigma$ is sufficiently close to 1. In particular, we will show that N(σ,T)$N(\sigma,T)$ can be bounded by an absolute constant when σ$\sigma$ is sufficiently close to the left edge of the Korobov–Vinogradov zero‐free region.
Chiara Bellotti
wiley   +1 more source

An elegant model of the geodesic flow on the modular surface

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract Caroline Series' [The modular surface and continued fractions, J. Lond. Math. Soc. (2), 31, no. 1, (1985), 69–80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular surface with the dynamics of the regular continued fraction, through a well‐chosen symbolic coding.
Pierre Arnoux, Thomas A. Schmidt
wiley   +1 more source

Some computational formulas related the Riemann zeta-function tails

Journal of Inequalities and Applications, 2016
In this paper we present two computational formulae for one kind of reciprocal sums related to the Riemann zeta-function at integer points s = 4 , 5 $s=4,5$ , which answers an open problem proposed by Lin (J. Inequal. Appl. 2016:32, 2016).
Hongmin Xu
doaj   +1 more source

Inequalities for Riemann’s zeta function

Portugaliae Mathematica, 2009
Let ζ and Λ be the Riemann zeta function and the von Mangoldt function, respectively. Further, let c > 0
openaire   +2 more sources

An inequality for the Selberg zeta-function, associated to the compact Riemann surface

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
We consider the absolute values of the Selberg zeta-function, associated to the compact Riemann surface, at places symmetric with respect to the line ℛ(s) = 1/2. We prove an inequality for the Selberg zeta-function, extending the result of R.
Belovas Igoris
doaj   +1 more source

The Nevanlinna Functions of the Riemann Zeta-Function

Journal of Mathematical Analysis and Applications, 1999
The author computes the Nevanlinna characteristic function, the Nevanlinna deficiencies for each \(a\) in \(\mathbb{C}\cup \{\infty\}\) and the Nevanlinna counting functions for the Riemann zeta-function. These results are of special interest because of the recent discovery of analogies between number theory and Nevanlinna theory.
openaire   +2 more sources

Joint universality of the Riemann zeta-function and Lerch zeta-functions

Nonlinear Analysis, 2013
In the paper, we prove a joint universality theorem for the Riemann zeta-function and a collection of Lerch zeta-functions with parameters algebraically independent over the field of rational numbers.
Antanas Laurinčikas, Renata Macaitienė˙   +1 more
doaj  

On the periodic zeta-function with rational parameter

Lietuvos Matematikos Rinkinys, 2011
We obtain an asymptotic formula with estimated error term for the fourth power moment of the periodic zeta-function with rational parameter.
Sondra Černigova
doaj   +1 more source

Partial Sums of the Hurwitz and Allied Functions and Their Special Values

Mathematics
We supplement the formulas for partial sums of the Hurwitz zeta-function and its derivatives, producing more integral representations and generic definitions of important constants.
Nianliang Wang, Ruiyang Li, Takako Kuzumaki   +2 more
doaj   +1 more source

On the Modulus of the Selberg Zeta-Functions in the Critical Strip

Mathematical Modelling and Analysis, 2015
We investigate the behavior of the real part of the logarithmic derivatives of the Selberg zeta-functions ZPSL(2,Z)(s) and ZC (s) in the critical strip 0 < σ < 1.
Andrius Grigutis, Darius Šiaučiūnas
doaj   +1 more source