Results 141 to 150 of about 71,113 (177)

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
openaire   +2 more sources

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

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.
openaire   +2 more sources

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.
openaire   +2 more sources

The Riemann zeta function on arithmetic progressions and denseness properties

European Journal of Mathematics, 2023
Junghun Lee
semanticscholar   +1 more source

ABOUT THE ABSCISSA OF CONVERGENCE OF THE ZETA FUNCTION OF A MULTIPLICATIVE ARITHMETICAL SEMIGROUP

Quaestiones Mathematicae, 2001
Mathematics Subject Classification (1991): 11N45 Keywords: zeta function, topological structures, algebraic structures, asymptotic, counting functions, abscissa, multiplicative arithmetical semigroup, additive arithmetical semigroup, semigroup, John Knopfmacher, radius of convergence, convergence Quaestiones Mathematicae 24(3) 2001, 363 ...
openaire   +5 more sources

Adelic Approach to the Zeta Function of Arithmetic Schemes in Dimension Two [PDF]

Moscow Mathematical Journal, 2008
This paper suggests a new approach to the study of the fun- damental properties of the zeta function of a model of elliptic curve over a global field. This complex valued commutative approach is a two-di- mensional extension of the classical adelic analysis of Tate and Iwasawa.
openaire   +1 more source

Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields [PDF]

, 2014
In the advanced course given at Centre de Recerca Matem`atica, consisting of twelve hour lectures from 22 February to 5 March 2010, we described results and discussed some open problems regarding the gamma and zeta functions in the function field context.
openaire   +1 more source