Results 31 to 40 of about 73,515 (215)

ZETA-VALUES OF ONE-DIMENSIONAL ARITHMETIC SCHEMES AT STRICTLY NEGATIVE INTEGERS [PDF]

Kyushu Journal of Mathematics, 2021
Let $X$ be an arithmetic scheme (i.e., separated, of finite type over $\operatorname{Spec} \mathbb{Z}$) of Krull dimension $1$.
A. Beshenov
semanticscholar   +1 more source

On the Cotangent Sums Related to Estermann Zeta Function and Arithmetic Properties of their Arguments

WSEAS Transactions on Mathematics, 2020
In this work we are interested by cotangent sum related to Estermann zeta function in rational arguments. In the first place we look at the maximum and the moment as they did H. Maier and M. Th.
M. Goubi
semanticscholar   +1 more source

THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE

Forum of Mathematics, Pi, 2020
For each $t\in \mathbb{R}$, we define the entire function $$\begin{eqnarray}H_{t}(z):=\int _{0}^{\infty }e^{tu^{2}}\unicode[STIX]{x1D6F7}(u)\cos (zu)\,du,\end{eqnarray}$$ where $\unicode[STIX]{x1D6F7}$ is the super-exponentially decaying function ...
BRAD RODGERS, TERENCE TAO
doaj   +1 more source

Another generalization of the gcd-sum function [PDF]

, 2013
We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group.
Tóth, László
core   +2 more sources

Multiplicity estimate for solutions of extended Ramanujan's system [PDF]

, 2011
We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan's classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive ...
Zorin, Evgeniy
core   +2 more sources

VALUES OF ZETA FUNCTIONS OF ARITHMETIC SURFACES AT

Journal of the Institute of Mathematics of Jussieu, 2022
AbstractWe show that the conjecture of [27] for the special value at$s=1$of the zeta function of an arithmetic surface is equivalent to the Birch–Swinnerton–Dyer conjecture for the Jacobian of the generic fibre.
Stephen Lichtenbaum, Niranjan Ramachandran   +1 more
openaire   +1 more source

Additive Cellular Automata and Volume Growth

Entropy, 2000
: A class of dynamical systems associated to rings of S-integers in rational function fields is described. General results about these systems give a rather complete description of the well-known dynamics in one-dimensional additive cellular automata ...
Thomas B. Ward
doaj   +1 more source

Spectral zeta functions of fractals and the complex dynamics of polynomials [PDF]

, 2005
We obtain formulas for the spectral zeta function of the Laplacian on symmetric finitely ramified fractals, such as the Sierpinski gasket, and a fractal Laplacian on the interval.
Teplyaev, Alexander
core   +3 more sources

The fourth moment of the Hurwitz zeta function [PDF]

Journal für die Reine und Angewandte Mathematik
We prove a sharp upper bound for the fourth moment of the Hurwitz zeta function ζ ⁢ ( s , α ) \zeta(s,\alpha) on the critical line when the shift parameter 𝛼 is irrational and of irrationality exponent strictly less than 3. As a consequence, we determine
Winston Heap, Anurag Sahay
semanticscholar   +1 more source

The Arithmetic Site [PDF]

, 2014
We show that the non-commutative geometric approach to the Riemann zeta function has an algebraic geometric incarnation: the "Arithmetic Site".
Connes, Alain, Consani, Caterina
core   +3 more sources