Results 11 to 20 of about 17,792 (168)
SPECIAL VALUES OF THE ZETA FUNCTION OF AN ARITHMETIC SURFACE [PDF]
Journal of the Institute of Mathematics of Jussieu, 2021 AbstractWe prove that the special-value conjecture for the zeta function of a proper, regular, flat arithmetic surface formulated in [6] at$s=1$is equivalent to the Birch and Swinnerton-Dyer conjecture for the Jacobian of the generic fibre. There are two key results in the proof.
Matthias Flach, Daniel Siebel
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On Zeta Functions of Arithmetically Defined Graphs
Finite Fields and Their Applications, 1999 Arithmetically defined graphs \(X(n)\), namely quotients of the Bruhat-Tits tree over a local field, are studied, using results from \textit{I. Rust} [Finite Fields Appl. 4, No. 4, 283-306 (1998; Zbl 0933.20033)]. Explicit formulae for the zeta function of \(X(n)\) for small \(n\) are given and, by employing techniques from \textit{K.
Ortwin Scheja
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Arithmetic progressions of zeros of the Riemann zeta function
Journal of Number Theory, 2005 It is widely believed that there are no arithmetic progressions of zeros of the Riemann zeta-function \(\zeta(s)\). In this paper the author proves the following result.
Machiel van Frankenhuijsen
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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 Excerpts from portions of the introduction: ``Let \(\Gamma\) be a discrete subgroup of \(\text{SL}_2(\mathbb{R})\) containing \(-1_2\) with finite covolume \(v(\Gamma\setminus{\mathfrak H})\), \({\mathfrak H}\) denoting the upper half plane. The Selberg zeta-function attached to \(\Gamma\) is defined by \[ Z_\Gamma(s):= \prod_{\{P\}_\Gamma} \prod_{m=0}^
Tsuneo Arakawa +2 more
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Riemann zeta function and arithmetic progression of higher order [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 Hamilton Brito +2 more
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The Riemann Zeta Function on Arithmetic Progressions [PDF]
Experimental Mathematics, 2012 We prove asymptotic formulas for the first discrete moment of the Riemann zeta function on certain vertical arithmetic progressions inside the critical strip. The results give some heuristic arguments for a stochastic periodicity that we observed in the phase portrait of the zeta function.
Jörn Steuding, Elías Wegert
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Eulerian series, zeta functions and the arithmetic of partitions
, 2020 Ph.D. dissertation (2018, Emory University, advisor Ken Ono) including joint work with Amanda Clemm, Marie Jameson, Ken Ono, Larry Rolen, Maxwell Schneider and Ian Wagner, 228 ...
Robert Schneider
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A $q$-series identity and the arithmetic of Hurwitz zeta functions [PDF]
Proceedings of the American Mathematical Society, 2002 Summary: 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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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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