4 papers
Connection between the Riemann zeta-function and random matrices via hyperfunctions
Masahiro Mine
Bohr pioneered the study of the statistical behavior of the Riemann zeta-function. A classical result by Bohr and Jessen revealed that the values of the Riemann zeta-function to th…
An upper bound for the number of smooth values of a polynomial and its applications
Masahiro Mine
We prove a new upper bound for the number of smooth values of a polynomial with integer coefficients. This improves Timofeev's previous result unless the polynomial is a product of…
A random variable related to the Hurwitz zeta-function with algebraic parameter
Masahiro Mine
In this paper, we introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. We prove a version of the lim…
New developments toward the Gonek Conjecture on the Hurwitz zeta-function
Masahiro Mine
In this paper, we prove a version of the universality theorem for the Hurwitz zeta-function in the case where the parameter is algebraic and irrational. Then we apply the result to…