Equalities, congruences, and quotients of zeta functions in Arithmetic Mirror Symmetry
, 2005 6 ...
C. Douglas Haessig
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A Further Generalisation of Sums of Higher Derivatives of the Riemann Zeta Function [PDF]
International Journal of Number Theory, 2021 We prove an asymptotic for the sum of $\zeta^{(n)} (\rho)X^{\rho}$ where $\zeta^{(n)} (s)$ denotes the $n$th derivative of the Riemann zeta function, $X$ is a positive real and $\rho$ denotes a non-trivial zero of the Riemann zeta function.
Andrew Pearce-Crump
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Arithmetic equivalence for function fields, the Goss zeta function and a generalisation
Journal of Number Theory, 2009 A theorem of Tate and Turner says that global function fields have the same zeta function if and only if the Jacobians of the corresponding curves are isogenous. In this note, we investigate what happens if we replace the usual (characteristic zero) zeta function by the positive characteristic zeta function introduced by Goss.
Gunther Cornelissen +2 more
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Representation zeta functions of compact p-adic analytic groups and arithmetic groups [PDF]
Duke Mathematical Journal, 2013 62 pages, minor ...
Nir Avni +3 more
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On the influence of the arithmetical character of the parameters for the Lerch zeta-function
Lietuvos matematikos rinkinys, 2002 There is not abstract.
Jolita Ignatavičiūtė
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Zeta Functions on Arithmetic Surfaces
, 2013 We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called mean-periodicity correspondence, which is comparable to the better known automorphicity conjectures for the ...
Thomas Oliver
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ZETA-VALUES OF ONE-DIMENSIONAL ARITHMETIC SCHEMES AT STRICTLY NEGATIVE INTEGERS [PDF]
Kyushu Journal of Mathematics, 2021 Let $X$ be an arithmetic scheme (i.e., separated, of finite type over $\operatorname{Spec} \mathbb{Z}$) of Krull dimension $1$.
A. Beshenov
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THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE
Forum of Mathematics, Pi, 2020 For each $t\in \mathbb{R}$, we define the entire function $$\begin{eqnarray}H_{t}(z):=\int _{0}^{\infty }e^{tu^{2}}\unicode[STIX]{x1D6F7}(u)\cos (zu)\,du,\end{eqnarray}$$ where $\unicode[STIX]{x1D6F7}$ is the super-exponentially decaying function ...
BRAD RODGERS, TERENCE TAO
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Arithmetic of Some Zeta Function Connected with the Eigenvalues of the Laplace–Beltrami Operator [PDF]
Advanced Studies in Pure Mathematics, 2018 Akio Fujii
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Stronger arithmetic equivalence
Discrete Analysis, 2021 Stronger arithmetic equivalence, Discrete Analysis 2021:23, 23 pp. An algebraic number field is a subfield $K$ of $\mathbb C$ that is finite-dimensional when considered as a vector space over $\mathbb Q$, which implies that every element of $K$ is ...
Andrew V. Sutherland
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