Results 101 to 110 of about 82,476 (235)

On the mean square of the periodic zeta-function. II

Nonlinear Analysis, 2015
In the paper, the error term in the Atkinson type formula for the periodic zeta-function in the critical strip is considered, and an asymptotic formula for its mean square is obtained. This formula generalizes that proved for the Riemann zeta-function.
Sondra Černigova, Antanas Laurinčikas
doaj   +1 more source

On the Riemann-Hilbert Problems [PDF]

arXiv, 1998
We discuss some topological aspects of the Riemann-Hilbert transmission problem and Riemann-Hilbert monodromy problem on Riemann surfaces. In particular, we describe the construction of a holomorphic vector bundle starting from the given representation of the fundamental group and investigate the local behaviour of connexions on this bundle.
arxiv  

Trace formula in noncommutative geometry and the zeros of the Riemann zeta function [PDF]

, 1998
. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances.
A. Connes
semanticscholar   +1 more source

Asymptotic estimates of large gaps between directions in certain planar quasicrystals

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract For quasicrystals of cut‐and‐project type in Rd$\mathbb {R}^d$, it was proved by Marklof and Strömbergsson [Int. Math. Res. Not. IMRN (2015), no. 15, 6588–6617; erratum, ibid. 2020] that the limit local statistical properties of the directions to the points in the set are described by certain SLd(R)$\operatorname{SL}_d(\mathbb {R})$‐invariant ...
Gustav Hammarhjelm, Andreas Strömbergsson, Shucheng Yu   +2 more
wiley   +1 more source

The limit of the Riemann zeta function and its nontrivial zeros [PDF]

arXiv, 2019
In this article, with a new approach, which is not discussed in the literature yet, the limit of the Riemann zeta function or Euler-Riemann zeta function is approximately explored by applying Dirichlet's rearrangement theorem for absolutely convergent series to the Riemann zeta function by rearranging its terms as geometric series for sufficiently ...
arxiv  

Jacobian elliptic fibrations on K3s with a non‐symplectic automorphism of order 3

Mathematische Nachrichten, Volume 298, Issue 5, Page 1758-1788, May 2025.
Abstract Let X$X$ be a K3 surface admitting a non‐symplectic automorphism σ$\sigma$ of order 3. Building on work by Garbagnati and Salgado, we classify the Jacobian elliptic fibrations on X$X$ with respect to the action of σ$\sigma$ on their fibers. If the fiber class of a Jacobian elliptic fibration on NS(X)$\operatorname{NS}(X)$ is fixed by σ$\sigma$,
Felipe Zingali Meira
wiley   +1 more source

A Geometric Proof of Riemann Hypothesis [PDF]

arXiv, 2003
Beginning from the formal resolution of Riemann Zeta function, by using the formula of inner product between two infinite-dimensional vectors in the complex space, the author proved the world's baffling problem -- Riemann hypothesis raised by German mathematician B. Riemann in 1859.
arxiv  

Two kinds of the reverse Hardy-type integral inequalities with the equivalent forms related to the extended Riemann zeta function

, 2018
Applying techniques of real analysis and weight functions, we study some equivalent conditions of two kinds of the reverse Hardy-type integral inequalities with a particular nonhomogeneous kernel.
M. Rassias, Bicheng Yang, Andrei M. Raigorodskii   +2 more
semanticscholar   +1 more source

Riemann surface of the Riemann zeta function

Journal of Mathematical Analysis and Applications
In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex $\adyn$-dimensional, customly denoted as $s$, another two are complex infinite dimensional, we denote it as $\b = \{b_n\}_{n=1}^{\infty}$ and $\z =\{z_n\}_{n=1}^{\infty}$. When $\b = \{1\}_{n=1}^{\infty}$ and $\z = \{\frac{1}{n}\}_{n=1}^
openaire   +3 more sources

CR$CR$ analysis via local uniform completion, a sharp maximum modulus principle and holomorphic extension

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract Using iterated uniform local completion, we introduce a notion of continuous CR$CR$ functions on locally closed subsets of reduced complex spaces, generalising both holomorphic functions and CR$CR$ functions on CR$CR$ submanifolds. Under additional assumptions of set‐theoretical weak pseudo‐concavity, we prove optimal maximum modulus ...
Mauro Nacinovich, Egmont Porten
wiley   +1 more source