An arithmetical mapping and applications to Ω-results for the Riemann zeta function [PDF]
Acta Arithmetica, 2009 In this paper we study the linear mapping that sends a sequence (an) to (bn) where bn = ∑ d|n d −αan/d. We investigate for which values of α this is a bounded operator from l to l and show the operator norm is closely connected to the Riemann zeta function.
Titus Hilberdink
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Universality theorems of the Selberg zeta functions for arithmetic groups
, 2023 20 ...
Yasufumi Hashimoto
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The Riemann Zeta Function on Vertical Arithmetic Progressions [PDF]
International Mathematics Research Notices, 2013 We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression $1/2 + i(an + b)$ with $a > 0$, $b$ real, exhibits a remarkable correspondance with the analogous continuous average and derive several consequences. For example, motivated by the linear independence conjecture, we show at least one third of
Xiannan Li, Maksym Radziwiłł
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Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2002 We obtain an arithmetic expression of the Selberg zeta function for cocompact Fuchsian group defined via an indefinite division quaternion algebra over $\mathbf{Q}$. As application to the prime geodesic theorem, we prove certain uniformity of the distribution.
Tsuneo Arakawa +2 more
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A $q$-series identity and the arithmetic of Hurwitz zeta functions [PDF]
Proceedings of the American Mathematical Society, 2002 Using a single variable theta identity, which is similar to the Jacobi Triple Product identity, we produce the generating functions for values of certain expressions of Hurwitz zeta functions at non-positive integers.
Gwynneth H. Coogan, Ken Ono
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Arithmetic calculus of Fourier transforms by Igusa local zeta functions [PDF]
Transactions of the American Mathematical Society, 1994 We show the possibility of explicit calculation of the Fourier transforms of complex powers of relative invariants of some prehomogeneous vector spaces over R \mathbb {R} by using the explicit form of p p -adic Igusa local zeta functions.
Tatsuo Kimura
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Discrete Ω-results for the Riemann zeta function [PDF]
Forum mathematicum, 2023 We study lower bounds for the Riemann zeta function ζ ( s ) {\zeta(s)} along vertical arithmetic progressions in the right-half of the critical strip.
Paolo Minelli, Athanasios Sourmelidis
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Unified Theory of Zeta-Functions Allied to Epstein Zeta-Functions and Associated with Maass Forms
Mathematics, 2023 In this paper, we shall establish a hierarchy of functional equations (as a G-function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional ...
Nianliang Wang +2 more
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Arithmetic expressions of Selberg's zeta functions for congruence subgroups
Journal of Number Theory, 2004 12 ...
Yasufumi Hashimoto
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An arithmetic zeta function respecting multiplicities
, 2020 In this paper, we study the arithmetic zeta function $$\mathscr{Z}_{\mathcal{X}}(s) = \prod_p \prod_{\substack{x \in \mathcal{X}_p \\ \text{closed}}} \Big( \frac{1}{1-|κ(x)|^{-s}} \Big)^{\mathfrak{m}_{p}(x)}$$ associated to a scheme $\mathcal{X}$ of finite type over $\mathbb{Z}$, where $κ(x)$ denotes the residue field and $\mathfrak{m}_{p}(x)$ the ...
Lukas Prader
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