Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Shibukawa, Genki"'
Autor:
Shibukawa, Genki
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 $x^{n} - 1$.
Comment: 8 pages, no figures
Comment: 8 pages, no figures
Externí odkaz:
http://arxiv.org/abs/2403.06263
Autor:
Shibukawa, Genki, Tsuchimi, Satoshi
By applying Slater's transformation formulas for the bilateral basic hypergeometric series ${}_2\psi_{2}$, we derive three type translation formulas for the generalized Zwegers' $\mu$-function (``continuous $q$-Hermite function'') which was introduce
Externí odkaz:
http://arxiv.org/abs/2305.08101
Autor:
Matsusaka, Toshiki, Shibukawa, Genki
We promote the recent research by Akiyama and Kaneko on the higher-order derivative values $\Phi_n^{(k)}(1)$ of the cyclotomic polynomials. This article focuses on Lehmer's explicit formula of $\Phi_n^{(k)}(1)/\Phi_n(1)$ as a polynomial of the Euler
Externí odkaz:
http://arxiv.org/abs/2305.00765
Autor:
Shibukawa, Genki, Tsuchimi, Satoshi
Publikováno v:
SIGMA 19 (2023), 014, 23 pages
We introduce a one parameter deformation of the Zwegers' $\mu$-function as the image of $q$-Borel and $q$-Laplace transformations of a fundamental solution for the $q$-Hermite-Weber equation. We further give some formulas for our generalized $\mu$-fu
Externí odkaz:
http://arxiv.org/abs/2206.15137
We give explicit expressions of some special values for the monomial symmetric polynomials as applications of symmetric functions and group determinants. We also prove some vanishing or non-vanishing properties of these special values.
Externí odkaz:
http://arxiv.org/abs/2203.14422
Autor:
Shibukawa, Genki
We present an explicit formula of the powers for the $2\times 2$ quantum matrices, that is a natural quantum analogue of the powers of the usual $2\times 2$ matrices. As applications, we give some non-commutative relations of the entries of the power
Externí odkaz:
http://arxiv.org/abs/2112.15464
Autor:
Shibukawa, Genki
We propose new Pieri type formulas for Jack polynomials, which is another kind of Pieri type formulas than the ones in the previous paper (G. Shibukawa, arXiv:2004.12875). From these new Pieri type formulas, we give yet another proof of difference an
Externí odkaz:
http://arxiv.org/abs/2010.04241
Autor:
Shibukawa, Genki
We extend the theorem by Olmsted (1945) and Carlitz-Thomas (1963) on rational values of trigonometric functions to powers of trigonometric functions.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2009.06583
Autor:
Shibukawa, Genki
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 $a^2+b^2+c^2=abcf(a,b,c)$.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2008.04061
Autor:
Shibukawa, Genki
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 explicit formulas and evaluate some singular values of the elliptic la
Externí odkaz:
http://arxiv.org/abs/2006.12034