On the multidimensional zeta functions associated with theta functions, and the multidimensional Appell polynomials
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DOI: 10.1002/mma.6075
Abstract: We define and study the multidimensional Appell polynomials associated with theta functions. For the trivial theta functions, we obtain the various well‐known Appell polynomials. Many other interesting examples are given. To push our study, by… read more here.
Keywords: zeta functions; appell polynomials; multidimensional appell; theta functions ... See more keywords
Selberg and Ruelle zeta functions for non-unitary twists
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DOI: 10.1007/s10455-017-9571-3
Abstract: In this paper we study the dynamical zeta functions of Ruelle and Selberg associated with the geodesic flow of a compact hyperbolic odd-dimensional manifold. These are functions of a complex variable s in some right… read more here.
Keywords: zeta functions; ruelle zeta; functions non; selberg ruelle ... See more keywords
Zeros of Riemann’s Zeta Functions in the Line z=1/2+it0
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DOI: 10.1007/s10948-019-05243-0
Abstract: It was found that, in addition to trivial zeros in points (z = − 2N, N = 1, 2…, natural numbers), the Riemann’s zeta function ζ(z) has zeros only on the line {$$ z=\frac{1}{2}+\mathrm{i}{\mathrm{t}}_0 $$, t0 is real}. All zeros are… read more here.
Keywords: zeta functions; line; zeros riemann; riemann zeta ... See more keywords
Motivic zeta functions on Q-Gorenstein varieties
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DOI: 10.1016/j.aim.2020.107192
Abstract: Abstract We study motivic zeta functions for Q -divisors in a Q -Gorenstein variety. By using a toric partial resolution of singularities we reduce this study to the local case of two normal crossing divisors… read more here.
Keywords: motivic zeta; gorenstein varieties; functions gorenstein; zeta functions ... See more keywords
Absolute zeta functions and absolute automorphic forms
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DOI: 10.1016/j.geomphys.2018.01.014
Abstract: Abstract We construct absolute zeta functions from absolute automorphic forms via the zeta regularization. We study analytic properties of absolute zeta functions. Especially we look at regularized Euler constants. We show a generalization of Euler’s… read more here.
Keywords: zeta functions; functions absolute; euler; absolute automorphic ... See more keywords
Resolution of a conjecture on the convexity of zeta functions
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DOI: 10.1016/j.jmaa.2018.12.034
Abstract: Abstract We settle a conjecture of Cerone and Dragomir on the concavity of the reciprocal of the Riemann zeta function on ( 1 , ∞ ) . It is further shown in general that reciprocals… read more here.
Keywords: zeta; convexity; cerone dragomir; resolution conjecture ... See more keywords
Identities for Bernoulli polynomials related to multiple Tornheim zeta functions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.03.071
Abstract: We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order convolutions, is a multiple of a specific product… read more here.
Keywords: tornheim zeta; bernoulli polynomials; multiple tornheim; zeta functions ... See more keywords
Gram points in the theory of zeta-functions of certain cusp forms
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DOI: 10.1016/j.jmaa.2021.125396
Abstract: Abstract In the paper, an analogue of the Gram points used in the theory of the Riemann zeta-function is introduced for zeta-functions of normalized Hecke-eigen cusp forms of weight κ. Some analytic properties of those… read more here.
Keywords: points theory; functions certain; zeta functions; cusp forms ... See more keywords
Limit formulas for multiple Hurwitz zeta functions
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DOI: 10.1016/j.jnt.2018.04.021
Abstract: Abstract We prove the limit formula for the multiple Hurwitz zeta function using absolute zeta functions. These formulas contain Euler's formula for the Euler constant proved in 1776. read more here.
Keywords: zeta functions; hurwitz zeta; limit formulas; formulas multiple ... See more keywords
Functional equations for Selberg zeta functions with Tate motives
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DOI: 10.1016/j.jnt.2021.05.012
Abstract: For a compact Riemann surface $M$ of genus $g\ge 2$, we study the functional equations of the Selberg zeta functions attached with the Tate motives $f$. We prove that certain functional equations hold if and… read more here.
Keywords: zeta functions; equations selberg; functions tate; selberg zeta ... See more keywords
Ihara zeta functions of coronae
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DOI: 10.1016/j.laa.2020.03.047
Abstract: Abstract We derive a factorization formula for the Ihara zeta function of the corona of two graphs. When the two graphs are regular, this factorization formula involves the graphs' adjacency spectra. As an application, we… read more here.
Keywords: zeta functions; graphs; ihara zeta; formula ... See more keywords