9 citations · 27 across the 16 of their papers we have counts for
4 papers · 1 filter
A New Aspect of Chebyshev's Bias for Elliptic Curves over Function Fields
Ikuya Kaneko, Shin-ya Koyama
This work considers the prime number races for non-constant elliptic curves over function fields. We prove that if , then there exist Chebyshev biases tow…
Towards the Deep Riemann Hypothesis for
Ikuya Kaneko, Shin-ya Koyama, Nobushige Kurokawa
We explicate the deep Riemann hypothesis for the general linear group on the convergence of normalised Euler products of standard -functions on the critical li…
Chebyshev's Bias for Ramanujan's -function via the Deep Riemann Hypothesis
Shin-ya Koyama, Nobushige Kurokawa
The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan's -function has a bias to being positive. This phenomenon is an analogue of Chebyshev's…
Chebyshev's Bias against Splitting and Principal Primes in Global Fields
Miho Aoki, Shin-ya Koyama
Reasons for the emergence of Chebyshev's bias were investigated. The Deep Riemann Hypothesis (DRH) enables us to reveal that the bias is a natural phenomenon for achieving a well-b…