arXiv subjects

Takahiro Wakasa

Publications and source records attributed to Takahiro Wakasa.

3 recordsLinked to original sources

arXiv2014

An explicit upper bound of the argument of Dirichlet $L$-functions on the generalized Riemann hypothesis

We prove an explicit upper bound of the function $S(t,χ)$, defined by the argument of Dirichlet $L$-functions. An explicit upper bound of the function $S_1(t)$, defined by the integral of the argument of the Riemann zeta-function, have already been obtained by A. Fujii. Our result is obtained by applying an idea of Fujii's result on $S_1(t)$. The constant part of the explicit upper bound of $S(t,χ)$ in this paper does not depend on a primitive Dirichlet character $χ\pmod {q>1}$.

math.NT↗

arXiv2013

Supremum of the function $S_1(t)$ on short intervals

We prove a lower bound on the supremum of the function $S_1(T)$ on short intervals, defined by the integration of the argument of the Riemann zeta-function. The same type of result on the supremum of $S(T)$ have already been obtained by Karatsuba and Korolev. Our result is based on the idea of the paper of Karatsuba and Korolev. Also, we show an improved Omega-result for a lower bound.

math.NT↗

arXiv2012

The explicit upper bound of the multiple integral of $S(t)$ on the Riemann Hypothesis

We prove explicit upper bounds of the function $S_m(T)$, defined by the repeated integration of the argument of the Riemann zeta-function. The explicit upper bound of $S(T)$ and $S_1(T)$ have already been obtained by A. Fujii. Our result is a generalization of Fujii's results.

math.NT↗