17 citations · 34 across the 22 of their papers we have counts for
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Transcendency of the determinant of the Riemann operator: on higher -groups
Nobushige Kurokawa, Hidekazu Tanaka
In previous papers we investigated basic properties of the determinant of the Riemann operator: acting on , where $…
Determinants of Riemann operators on Quillen's higher -groups: periodicity
Nobushige Kurokawa, Hidekazu Tanaka
In a previous paper [KT] we introduced determinant of the Riemann operator on Quillen's higher -groups of the integer ring of an algebraic number field . We showed that the d…
Riemann operators on higher -groups
Nobushige Kurokawa, Hidekazu Tanaka
We introduce Riemann operators acting on Quillen's higher --groups for the integer ring of an algebraic number field . Especially we prove that gamma factors o…
Variations on theorems of Mertens
Nobushige Kurokawa, Hidekazu Tanaka
We present variations on theorems of Mertens as special cases of Density Hypothesis. Moreover, we study a Serre's estimate concerning Lang-Weil estimate.
Towards the Deep Riemann Hypothesis for
Ikuya Kaneko, Shin-ya Koyama, Nobushige Kurokawa
We explicate the deep Riemann hypothesis for the general linear group on the convergence of normalised Euler products of standard -functions on the critical li…
Chebyshev's Bias for Ramanujan's -function via the Deep Riemann Hypothesis
Shin-ya Koyama, Nobushige Kurokawa
The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan's -function has a bias to being positive. This phenomenon is an analogue of Chebyshev's…