arXiv subjects
Publications and source records attributed to Toshiki Matsusaka.
It is well known that real zeros of the Riemann zeta function are negative even integers. As for real zeros of the Hurwitz zeta function, T. Nakamura recently gave an existence condition in the intervals (0,1) and (-1,0). We generalize this result for all negative real numbers.
The elliptic modular j function enjoys many beautiful properties. Its Fourier coefficients are related to the Monster group, and its CM values generate abelian extensions over imaginary quadratic fields. Kaneko gave an arithmetic formula for the Fourier coefficients expressed in terms of the traces of the CM values. In this article, we are concerned with analogues of Kaneko's result for the McKay-Thompson series of square-free level.
We give arithmetic formulas for the coefficients of Hauptmoduln of higher levels as analogues of Kaneko's result. We also obtain their asymptotic formulas by employing Murty-Sampath's method.