4 citations · 10 across the 25 of their papers we have counts for
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A generalization of a Ramanujan's exercise and Fibonacci polynomials
Genki Shibukawa
We give a generalization of a Ramanujan's exercise for high school students. Our results can be regarded as a variation of the factorization formula of .
Curious congruences for cyclotomic polynomials II
Toshiki Matsusaka, Genki Shibukawa
We promote the recent research by Akiyama and Kaneko on the higher-order derivative values of the cyclotomic polynomials. This article focuses on Lehmer's explicit f…
Rational values of powers of trigonometric functions
Genki Shibukawa
We extend the theorem by Olmsted (1945) and Carlitz-Thomas (1963) on rational values of trigonometric functions to powers of trigonometric functions.
An equivalent condition for the Markov triples and the Diophantine equation
Genki Shibukawa
We propose an equivalent condition for the Markov triples, which was mentioned by H. Rademacher essentially. As an application, we study the solvability of the Diophantine equation…
Some singular values of the elliptic lambda function and incredible cubic identities
Genki Shibukawa
We propose three kinds of explicit formulas for the elliptic lambda function by the elliptic modular function. Further, we derive incredible cubic identities as a corollary of our…
An elliptic analogue of Fukuhara's trigonometeric identities
Genki Shibukawa
We obtain new elliptic function identities, which are an elliptic analogue of Fukuhara's trigonometric identities. We show that the coefficients of Laurent expansions at of o…
Some arithmetic properties of an elliptic Dedekind sum
Genki Shibukawa
We give an explicit expression of the elliptic classical Dedekind sum which is a special case of multiple elliptic Dedekind sums introduced by Egami. We also determine the denomina…