5 citations · 18 across the 12 of their papers we have counts for
12 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…
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…
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…
On the value-distribution of the logarithms of symmetric power L-functions in the level aspect
Philippe Lebacque, Kohji Matsumoto, Masahiro Mine +1
We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under c…
Large deviations for values of -functions attached to cusp forms in the level aspect
Masahiro Mine
We study the distribution of values of automorphic -functions in a family of holomorphic cusp forms with prime level. We prove an asymptotic formula for a certain density functi…
On the value-distribution of iterated integrals of the logarithm of the Riemann zeta-function II: probabilistic aspects
Kenta Endo, Shōta Inoue, Masahiro Mine
In this paper, we discuss the value-distribution of the Riemann zeta-function. The authors give some results for the discrepancy estimate and large deviations in the limit theorem…
Probability density functions attached to random Euler products for automorphic -functions
Masahiro Mine
In this paper, we study the value-distributions of -functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic -functions with probabili…
The value-distribution of Artin -functions associated with cubic fields in conductor aspect
Masahiro Mine
Arising from the factorizations of Dedekind zeta-functions of cubic fields, we obtain Artin -functions of certain two-dimensional representations. In this paper, we study the va…
On certain mean values of logarithmic derivatives of -functions and the related density functions
Masahiro Mine
We study some "density function" related to the value-distribution of -functions. The first example of such a density function was given by Bohr and Jessen in 1930s for the Riem…
The density function for the value-distribution of the Lerch zeta-function and its applications
Masahiro Mine
The probabilistic study of the value-distributions of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a certain probability measure re…
On the value-distributions of logarithmic derivatives of Dedekind zeta functions
Masahiro Mine
We study the distributions of values of the logarithmic derivatives of the Dedekind zeta functions on a fixed vertical line. The main object is determining and investigating the de…