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Zeroes of Zeta Functions and Symmetry
, 1999
"... Hilbert and Polya suggested that there might be a natural spectral interpretation of the zeroes of the Riemann Zeta function. While at the time there was little evidence for this, today the evidence is quite convincing. Firstly, there are the “function field” analogues, that is zeta functions of cur ..."
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Cited by 175 (2 self)
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Hilbert and Polya suggested that there might be a natural spectral interpretation of the zeroes of the Riemann Zeta function. While at the time there was little evidence for this, today the evidence is quite convincing. Firstly, there are the “function field” analogues, that is zeta functions
Heught zeta functions of . . .
, 2008
"... We study analytic properties of height zeta functions of equivariant ..."
Zeta functions of finite graphs
 J. MATH. SCI. UNIV. TOKYO
, 2000
"... Poles of the Ihara zeta function associated with a finite graph are described by graphtheoretic quantities. Elementary proofs based on the notions of oriented line graphs, PerronFrobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta f ..."
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Cited by 39 (1 self)
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Poles of the Ihara zeta function associated with a finite graph are described by graphtheoretic quantities. Elementary proofs based on the notions of oriented line graphs, PerronFrobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta
Convergence of zeta functions of graphs
 t=1 t=1 FUNCTIONS OF INFINITE GRAPH BUNDLES 17
"... Abstract. The L 2zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the L 2zeta function of Y. ..."
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Cited by 6 (0 self)
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Abstract. The L 2zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the L 2zeta function of Y.
Growth of the Lerch zetafunction
"... Abstract. It is believed that the Lindelöf hypothesis is also true for the Lerch zetafunction. Here we present results supporting this conjecture. We first consider the growth of the Lerch zetafunction assuming the generalized Lindelöf hypothesis for Dirichlet Lfunctions. We next prove that Hux ..."
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Abstract. It is believed that the Lindelöf hypothesis is also true for the Lerch zetafunction. Here we present results supporting this conjecture. We first consider the growth of the Lerch zetafunction assuming the generalized Lindelöf hypothesis for Dirichlet Lfunctions. We next prove
THE MOMENT ZETA FUNCTION AND APPLICATIONS
, 2002
"... Abstract. Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the moment zeta function of a probability distribution, and study in depth some asymptotic properties of the moment zeta function of those distributions suppo ..."
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Abstract. Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the moment zeta function of a probability distribution, and study in depth some asymptotic properties of the moment zeta function of those distributions
Hypergeometric Zeta Functions
, 2005
"... This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the int ..."
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Cited by 6 (4 self)
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This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including
Rationality of partial zeta functions
 Indagationes Mathematicae
"... We prove that the partial zeta function introduced in [9] is a rational function, generalizing Dwork’s rationality theorem. 1 ..."
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Cited by 3 (3 self)
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We prove that the partial zeta function introduced in [9] is a rational function, generalizing Dwork’s rationality theorem. 1
Bartholdi Zeta Functions for Hypergraphs
 THE ELECTRONIC JOURNAL OF COMBINATORICS
, 2006
"... Recently, Storm [8] defined the IharaSelberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of ..."
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Cited by 1 (0 self)
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Recently, Storm [8] defined the IharaSelberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function
THE ERROR ZETA FUNCTION
, 2006
"... This paper investigates a new special function referred to as the error zeta function. Derived as a fractional generalization of hypergeometric zeta functions, the error zeta function is shown to exhibit many properties analogous to its hypergeometric counterpart. These new properties are treated i ..."
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This paper investigates a new special function referred to as the error zeta function. Derived as a fractional generalization of hypergeometric zeta functions, the error zeta function is shown to exhibit many properties analogous to its hypergeometric counterpart. These new properties are treated
Results 1  10
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