Results 161 to 170 of about 545,098 (196)

Arithmetical identities and zeta‐functions

Mathematische Nachrichten, 2010
AbstractIn this paper we establish a class of arithmetical Fourier series as a manifestation of the intermediate modular relation, which is equivalent to the functional equation of the relevant zeta‐functions. One of the examples is the one given by Riemann as an example of a continuous non‐differentiable function.
Yoshio Tanigawa   +3 more
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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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The values of the Riemann zeta-function on generalized arithmetic progressions

Archiv der Mathematik, 2018
We study the mean of the values of the zeta-function on a generalized arithmetic progression on the critical line.
Selin Selen Özbek, Jörn Steuding
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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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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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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 ...
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