11 papers
Some results on naive transcendence in the ring of integers modulo infinitely large primes
Toshiki Matsusaka, Shin-ichiro Seki
This paper presents various transcendence results in the ring of integers modulo infinitely large primes . In the ring , one can consider two notions of t…
On finite analogues of DobiÅski's formula and of Euler's constant via Gregory polynomials
Toshiki Matsusaka, Taichi Miyazaki, Shunta Yara
We study a finite analogue of DobiÅski's formula, which is related to the Napier constant , and its Bessel-type generalizations. Furthermore, using Gregory polynomials, we exte…
Poly-Bernoulli numbers from shifted log-sine integrals
Toshiki Matsusaka
In 1999, Arakawa and Kaneko introduced a zeta function whose special values at negative integers yield the poly-Bernoulli numbers and investigated its relation to multiple zeta val…
On the Alexander polynomials of modular knots
Soon-Yi Kang, Toshiki Matsusaka, Kyungbae Park
Closed geodesics associated with indefinite binary quadratic forms, or equivalently with real quadratic irrationals, have long been studied as geometric …
The Fourier coefficients and singular moduli of the elliptic modular function , revisited
Toshiki Matsusaka
Kaneko's formula expresses the Fourier coefficients of the elliptic modular -function as finite sums of singular moduli. First published as a short article in 1996, it was prese…
Denominator identity for the affine Lie superalgebra and indefinite theta functions
Toshiki Matsusaka, Miyu Suzuki
In 1994, Kac and Wakimoto found the denominator identity for classical affine Lie superalgebras, generalizing that for affine Lie algebras. As an application, they obtained power s…