Keiju Sono

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20162024

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math.NT2024

An explicit lower bound for large gaps between some consecutive primes

Keiju Sono

Let $p_{n}$ denote the $n$ th prime and for any fixed positive integer $k$ and $X \geq 2$ , put \[ G_{k}(X):=\max _{p _{n+k}\leq X} \min \{ p_{n+1}-p_{n}, \ldots , p_{n+k}-p_{n+k-1} \…

math.NT2021

The second moment of Dirichlet twists of a $GL_{4}$ automorphic $L$ -function

Keiju Sono

In this paper, we give an asymptotic formula for the second moment of Dirichlet twists of an automorphic $L$ -function $L (s, π)$ on the critical line averaged over characters and co…

math.NT2021

Zeros of Dirichlet $L$ -functions on the critical line

Keiju Sono

In this paper, we estimate the proportion of zeros of Dirichlet $L$ -functions on the critical line. Using Feng's mollifier and an asymptotic formula for the mean square of Dirichle…

math.NT2016

Small gaps between the set of products of at most two primes

Keiju Sono

In this paper, we apply the method of Maynard and Tao to the set of products of two distinct primes (E2-numbers). We obtain several results on the distribution of E2-numbers and pr…

An explicit lower bound for large gaps between some consecutive primes

The second moment of Dirichlet twists of a GL4​ automorphic L-function

Zeros of Dirichlet L-functions on the critical line

Small gaps between the set of products of at most two primes

The second moment of Dirichlet twists of a $GL_{4}$ automorphic $L$ -function

Zeros of Dirichlet $L$ -functions on the critical line