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June 2022 Chebyshev’s bias for Ramanujan’s $\tau$-function via the Deep Riemann Hypothesis
Shin-ya Koyama, Nobushige Kurokawa
Proc. Japan Acad. Ser. A Math. Sci. 98(6): 35-39 (June 2022). DOI: 10.3792/pjaa.98.007

Abstract

The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan’s $\tau$-function has a bias to being positive. This phenomenon is an analogue of Chebyshev’s bias.

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Shin-ya Koyama. Nobushige Kurokawa. "Chebyshev’s bias for Ramanujan’s $\tau$-function via the Deep Riemann Hypothesis." Proc. Japan Acad. Ser. A Math. Sci. 98 (6) 35 - 39, June 2022. https://doi.org/10.3792/pjaa.98.007

Information

Published: June 2022
First available in Project Euclid: 26 May 2022

Digital Object Identifier: 10.3792/pjaa.98.007

Subjects:
Primary: 11M41

Keywords: Chebyshev’s bias , Deep Riemann Hypothesis , Ramanujan’s $\tau$-function , zeta functions

Rights: Copyright © 2022 The Japan Academy

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Vol.98 • No. 6 • June 2022
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