arXiv subjects

Michitomo Nishizawa

Publications and source records attributed to Michitomo Nishizawa.

8 recordsLinked to original sources

arXiv2009

The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra $gl_N$. The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a shifted version of the singular polynomials studied by Dunkl. We prove that our solutions contain those obtained as a scaling limit of matrix elements of the vertex operators of level one.

math.QA↗

arXiv2004

Infinite Product Representations fot Multiple Gamma Function

Two kinds of infinite product representations for Vignéras multiple gamma function are presented. As an application of these formulas, a multiplication formula for the function is derived.

math.CA↗

arXiv2004

Connection formulas for the confluent hypergeometric functions and the functional relation for the Hurwitz zeta function

The functional relation of the Hurwitz zeta function is proved by using the connection problem of the confluent hypergeometric equation.

math.NT↗

arXiv1996

Integral soluitons of q-difference equations of the hypergeometric type with |q|=1

Two integral solutions of q-difference equations of the hypergeometric type with |q|=1 are constructed by using the double sine function. One is an integral of the Barnes type and the other is of the Euler type.

q-alg↗

arXiv1996

The multiple gamma functions and the multiple q-gamma functions

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vignéras multiple gamma functions by considering the classical limit of the multiple q-gamma functions.

q-alg↗

arXiv1996

The multiple gamma function and its q-analogue

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vignéras multiple gamma function by considering the classical limit of the multiple q-gamma function.

q-alg↗

arXiv1995

On a q-analogue of the multiple gamma functions

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.

q-alg↗

arXiv1994

Quantum groups and zeta-functions

A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas of some relevant $q$-functions are discussed.

hep-th↗