4 papers
The Fine-Structure Hierarchy of Prime Biases and the Universal Dominance of
Shin-ya Koyama
We investigate the deterministic hierarchy of prime distribution biases in arithmetic progressions modulo using a regularized spectral approach. Classical studies on Chebyshev'…
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…
Chebyshev's bias for modular forms
Shin-ya Koyama, Arshay Sheth
We study Chebyshev's bias for the signs of Fourier coefficients of cuspidal newforms on . Our main result shows that the bias towards either sign is completely determined…
Quantum Unique Ergodicity for Eisenstein Series on Bruhat-Tits Buildings
Ikuya Kaneko, Shin-ya Koyama
We prove the quantum unique ergodicity conjecture for Eisenstein series over function fields in the level aspect. Adapting the machinery of Luo-Sarnak (1995), we employ the spectra…