6 papers
Explicit extreme values of the argument of the Riemann zeta-function
ShÅta Inoue, Hirotaka Kobayashi, Yuichiro Toma
We investigate explicit extreme values of the argument of the Riemann zeta-function in short intervals. As an application, we improve the result of Conrey and Turnage-Butterbaugh c…
Bounds for moments of quadratic character sums and theta functions
Marc Munsch, Yuichiro Toma
In this paper, we investigate the size of moments of quadratic character sums averaged over the family of fundamental discriminants. We obtain an asymptotic formula for all integer…
Moments of quadratic Dirichlet character sums
Yuichiro Toma
We consider moments of higher powers of quadratic Dirichlet character sums. In a restricted region, we give their asymptotic behavior by using de la Bretèche's multivariable Taube…
Mean square of inverses of Dirichlet -functions involving conductors
Iu-Iong Ng, Yuichiro Toma
We deal with negative square moments of Dirichlet -functions. Summing over characters modulo , we obtain an asymptotic formula for the negative second moment of inv…
On the moments of averages of quadratic twists of the Möbius function
Yuichiro Toma
We consider the moment of quadratic twists of the Möbius function of the form \[ S_k(X,Y) = \sum_{d\leq X} \left( \sum_{n\leq Y} \left(\frac{8d}{n}\right) μ(n)\right)^k, \] where…
Recovering short generators via negative moments of Dirichlet -functions
Iu-Iong Ng, Yuichiro Toma
In 2016, Cramer, Ducas, Peikert and, Regev proposed an efficient algorithm for recovering short generators of principal ideals in -th cyclotomic fields with being a prime po…