Proc. Japan Acad. Ser. A Math. Sci. 98 (6), 35-39, (June 2022) DOI: 10.3792/pjaa.98.007
Shin-ya Koyama, Nobushige Kurokawa
KEYWORDS: zeta functions, Deep Riemann Hypothesis, Ramanujan’s $\tau$-function, Chebyshev’s bias, 11M41
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.