9 citations · 27 across the 16 of their papers we have counts for
16 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 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 b…
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…
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…
Variations of Ramanujan's Euler Products
Shin-ya Koyama, Nobushige Kurokawa
We study the meromorphy of various Euler products of degree two attached to cusp forms including Ramanujan's -function.
Rigidity of Euler Products
Shin-ya Koyama, Nobushige Kurokawa
We report a simple rigidity theorem for certain Euler products.
Functional equations for Selberg zeta functions with Tate motives
Shin-ya Koyama, Nobushige Kurokawa
For a compact Riemann surface of genus , we study the functional equations of the Selberg zeta functions attached with the Tate motives . We prove that certain funct…
Simple functional equations for generalized Selberg zeta functions with Tate motives
Shin-ya Koyama, Nobushige Kurokawa
We prove that for a compact locally symmetric Riemannian space of rank 1 there exist infinitely many automorphic Tate motives such that the generalized Selberg zeta functio…
Correction to: Equidistribution of Eisenstein Series in the Level Aspect
Ikuya Kaneko, Shin-ya Koyama
The second author formulated quantum unique ergodicity for Eisenstein series in the prime level aspect in "Equidistribution of Eisenstein series in the level aspect", Commun. Math.…
Euler products of Selberg zeta functions in the critical strip
Ikuya Kaneko, Shin-ya Koyama
For any congruence subgroup of the modular group, we extend the region of convergence of the Euler products of the Selberg zeta functions beyond the boundary Re s = 1, if they are…
Triple mean values of Witten -functions
Shin-ya Koyama, Nobushige Kurokawa
Mean values of Witten -functions in the "character" aspect are investigated. After giving a general formula for mean values with the first and the second power, we explicitly ca…
Counting and zeta functions over F1
Anton Deitmar, Shin-Ya Koyama, Nobushige Kurokawa
A new interpretation of zeta functions is given for F1-schemes which do not satisfy Soulé's condition. Functional equations for reductive groups are computed and a new definition o…
Euler Products beyond the Boundary
Taro Kimura, Shin-ya Koyama, Nobushige Kurokawa
We investigate the behavior of the Euler products of the Riemann zeta function and Dirichlet L-functions on the critical line. A refined version of the Riemann hypothesis, which is…