Experimental Mathematics

The Riemann Zeta Function on Arithmetic Progressions

J örn Steuding and Elias Wegert

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Abstract

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.

Article information

Source
Experiment. Math., Volume 21, Issue 3 (2012), 235-240.

Dates
First available in Project Euclid: 13 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.em/1347541274

Mathematical Reviews number (MathSciNet)
MR2988576

Zentralblatt MATH identifier
1295.11089

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Keywords
Riemann zeta function value distribution arithmetic progression

Citation

Steuding, J örn; Wegert, Elias. The Riemann Zeta Function on Arithmetic Progressions. Experiment. Math. 21 (2012), no. 3, 235--240. https://projecteuclid.org/euclid.em/1347541274


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