>>249
>https://www.gensu.jp/product/%e7%8f%be%e4%bb%a3%e6%95%b0%e5%ad%a6%e3%80%802026%e5%b9%b43%e6%9c%88%e5%8f%b7%e3%80%80%e7%ac%ac59%e5%b7%bb%e7%ac%ac3%e5%8f%b7%e9%80%9a%e5%b7%bb711%e5%8f%b7/
>現代数学　2026年3月号　第59巻第3号通巻711号
>・BSD 予想から深リーマン予想への眺望　チェビシェフの偏りと平方剰余・非剰余　　　青木美穂

買ってきました。読んでますが
なかなかむずい
どうも 下記の 小山信也先生との共著論文の解説だというところまでは
分りました　（＾＾；

(参考)
https://researchmap.jp/koyama/published_papers
小山 信也 論文 82
Chebyshev's Bias against Splitting and Principal Primes in Global Fields
Miho Aoki, Shin-ya Koyama
Journal of Number Theory 245 233-262 2023年1月

https://www.sciencedirect.com/science/article/abs/pii/S0022314X22002335?via%3Dihub
Journal of Number Theory
Volume 245, April 2023, Pages 233-262
General Section
Chebyshev's bias against splitting and principal primes in global fields
Dedicated to Professor Nobushige Kurokawa on his 70th birthday
Author links open overlay panel
Miho Aoki a
Shin-ya Koyama b

Highlights
•Chebyshev's bias is defined by an asymptotic formula of a weighted counting function.
•The Deep Riemann Hypothesis is essential for considering Chebyshev's bias.
•Chebyshev's bias is equivalent to the convergence of Euler products at the center.

Abstract
A reason for the emergence of Chebyshev's bias is investigated. The Deep Riemann Hypothesis (DRH) enables us to reveal that the bias is a natural phenomenon for making a well-balanced disposition of the whole sequence of primes, in the sense that the Euler product converges at the center. By means of a weighted counting function of primes, we succeed in expressing magnitudes of the deflection by a certain asymptotic formula under the assumption of DRH, which gives a new formulation of Chebyshev's bias.
For any Galois extension of global fields and for any element σ in the Galois group, we establish a criterion of the bias of primes whose Frobenius elements are equal to σ under the assumption of DRH. As an application we obtain a bias toward non-splitting and non-principle primes in abelian extensions under DRH. In positive characteristic cases, DRH is proved, and all these results hold unconditionally.

Introduction
Chebyshev's bias is the phenomenon that there tend to be more primes of the form
than of the form
. In fact, if denoting by
the number of primes
such that
, then the inequality
holds for any x less than 26861, which is the first prime number violating the inequality (1.1). However, the both sides draw equal at the next prime 26863, and
gets ahead again until 616841.