4 citations · 10 across the 25 of their papers we have counts for
26 papers
Monotonicity of solutions to second order linear difference equations with constant coefficients
Yoshiaki Goto, Genki Shibukawa
We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the…
Notes on twisted homology and cohomology groups for the Wirtinger integral
Yoshiaki Goto, Genki Shibukawa
The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand is given by a product of complex powers of theta functions. We stu…
The intertwining property for -Laguerre processes and integral operators for Jack polynomials
Yosuke Kawamato, Genki Shibukawa
The aim of this paper is to study intertwining relations for Laguerre process with inverse temperature and parameter . We introduce a Markov kernel that depends on b…
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 .
The generalized Zwegers' -function and transformation formulas for the bilateral basic hypergeometric series
Genki Shibukawa, Satoshi Tsuchimi
By applying Slater's transformation formulas for the bilateral basic hypergeometric series , we derive three type translation formulas for the generalized Zwegers' -f…
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…
A Generalization of Zwegers' -Function According to the -Hermite-Weber Difference Equation
Genki Shibukawa, Satoshi Tsuchimi
We introduce a one parameter deformation of the Zwegers' -function as the image of -Borel and -Laplace transformations of a fundamental solution for the -Hermite-Weber…
Principal Specialization of Monomial Symmetric Polynomials and Group Determinants of Cyclic Groups
Naoya Yamaguchi, Yuka Yamaguchi, Genki Shibukawa
In this paper, we study the principal specialization of monomial symmetric polynomials and investigate the special values of these polynomials at \[ ζ_{(n,k)} := ( 1, ζ_n, ζ_n^2, \…
An explicit formula of powers of the quantum matrices and its applications
Genki Shibukawa
We present an explicit formula of the powers for the quantum matrices, that is a natural quantum analogue of the powers of the usual matrices. As applicatio…
Raising type twisted Pieri formulas for Jack polynomials and their applications to interpolation Jack polynomials
Genki Shibukawa
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 the…
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…
New Pieri Type Formulas for Jack Polynomials and their Applications to Interpolation Jack Polynomials
Genki Shibukawa
We present new Pieri type formulas for Jack polynomials. As an application, we give a new derivation of higher order difference equations for interpolation Jack polynomials origina…
A revisit to periodic continuants
Genki Shibukawa
We give a simple proof of some explicit formulas of periodic continuants by Chebyshev polynomials of the second kind given by Rozsa.
New identities for some symmetric polynomials, and a higher order analogue of the Fibonacci and Lucas numbers
Genki Shibukawa
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
Multivariate Bernoulli polynomials
Genki Shibukawa
We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion fo…
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…
New trigonometric identities and reciprocity laws of generalized Dedekind sums II
Genki Shibukawa
We obtain new trigonometric identities, which are product-to-sum type formulas for derivative of the cosecant and cotangent functions. Further, from specializations of our formulas…
Bilateral zeta functions associated with the multiple sine functions
Genki Shibukawa
We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties…
New trigonometric identities and reciprocity laws of generalized Dedekind sums
Genki Shibukawa
We obtain new trigonometric identities, which are some product-to-sum type formulas for the higher derivative of the cotangent and cosecant functions. Further, from specializations…
Multivariate circular Jacobi polynomials
Genki Shibukawa
We introduce a new multivariate orthogonal polynomial which is a 2-parameter deformation of the spherical polynomial by harmonic analysis on symmetric cone. This is also regarded a…
Multivariate Meixner, Charlier and Krawtchouk polynomials
Genki Shibukawa
We introduce some multivariate analogues of Meixner, Charlier and Krawtchouk polynomials, and establish their main properties, that is, duality, degenerate limits, generating funct…