Results 181 to 190 of about 73,515 (215)

RUELLE TYPE ZETA FUNCTIONS FOR TORI AND SOME ARITHMETICS

International Journal of Mathematics, 2004
We introduce various Ruelle type zeta functions ζL(s) according to a choice of homogeneous "length functions" for a lattice L in [Formula: see text] via Euler products. The logarithm of each ζL(s) yields naturally a certain arithmetic function. We study the asymptotic distribution of averages of such arithmetic functions.
Kurokawa Nobushige, Wakayama Masato
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A PROBABILISTIC ZETA FUNCTION FOR ARITHMETIC GROUPS

International Journal of Algebra and Computation, 2005
A profinite group G is positively finitely generated (PFG) if for some k, the probability P(G,k) that k random elements generate G is positive. It was conjectured that if G is PFG, then the function P(G,k) can be interpolated to an analytic function defined in some right half-plane.
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Studying the upper bound of Beurling zeta function in the strip (0,1)

Journal of Interdisciplinary Mathematics
During the third decade of the last century, Arne Beurling stated the sense of the generalized prim systems. He said that any positive, increasingly real sequence started from any number greater than one precisely, and this sequence is called Beurling ...
Safa Mohsen Abd Alzahra, Faez A. Al-Maamori   +1 more
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Mean value inequalities for the Riemann zeta function

Integral transforms and special functions
We study monotonicity properties of the functions \[ x\mapsto \zeta(x)+\zeta(1/x) \quad\mbox{and}\quad x\mapsto \frac{1}{\zeta(x)}+\frac{1}{\zeta(1/x)} \]x↦ζ(x)+ζ(1/x)andx↦1ζ(x)+1ζ(1/x) and apply our results to obtain sharp bounds for the arithmetic ...
H. Alzer, Man Kam Kwong
semanticscholar   +1 more source

Arithmetic Consequences of the GUE Conjecture for Zeta Zeros

The Michigan mathematical journal
Conditioned on the Riemann hypothesis, we show that the conjecture that the zeros of the Riemann zeta function resemble the eigenvalues of a random matrix is logically equivalent to a statement about the distribution of primes.
B. Rodgers
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Primes, Arithmetic Functions, and the Zeta Function

2002
In this chapter we will discuss properties of primes and prime decomposition in the ring A = F[T]. Much of this discussion will be facilitated by the use of the zeta function associated to A. This zeta function is an analogue of the classical zeta function which was first introduced by L.
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On values of Dedekind zeta function

Proceedings - Mathematical Sciences, 2023
Dhananjaya Sahu
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The Arithmetic of Certain Zeta Functions and Automorphic Forms on Orthogonal Groups

The Annals of Mathematics, 1980
Q(z) = ,Q?(&2 of an integral weight > 0; k is a positive integer; * is an embedding of K into C; r is an element of K0 such that Id2 is its only positive conjugate; 4D-b(* + Ap) + ,cpgp, where b and c, are non-negative integers, p is the complex conjugation, and {qp} is the set of all embeddings of K into C other than * and Ap.
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On the zetafunction of an arithmetical semigroup

Mathematische Zeitschrift, 2003
The concept of a commutative additive arithmetical semigroup \(A\) was introduced by John Knopfmacher. Associated to \(A\) there is a Zeta function \(Z(x)\) which reflects the arithmetical properties of \(A\). It is defined by \[ Z(x)=\sum_{n=0}^\infty f(n)x^n=\prod_{n=1}^\infty(1-x^n)^{-g(n)}, \] where \(f(n)\) resp.
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Special Values of Zeta-Functions for Proper Regular Arithmetic Surfaces

2019
We explicate Flach's and Morin's special value conjectures in [8] for proper regular arithmetic surfaces π : X → Spec Z and provide explicit formulas for the conjectural vanishing orders and leading Taylor coefficients of the associated arithmetic zeta-functions.
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