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Masanobu Kaneko

Publications and source records attributed to Masanobu Kaneko.

30 records · Page 2Linked to original sources
arXiv2016

On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is apparent. Secondly we give an analytic proof of the duality from the viewpoint of our previous study of zeta-functions of Arakawa-Kaneko type. As an application, we give a formula that relates poly-Bernoulli numbers to the Genocchi numbers.

math.NT↗
arXiv2015

On multiple zeta values of extremal height

We give three identities involving multiple zeta values of height one and of maximal height; an explicit formula for the height-one multiple zeta values, a regularized sum formula, and a sum formula for the multiple zeta values of maximal height.

math.NT↗
arXiv2012

The Ramanujan-Serre differential operators and certain elliptic curves

For several congruence subgroups of low levels and their conjugates, we derive differential equations satisfied by the Eisenstein series of weight 4 and relate them to elliptic curves, whose associated new forms of weight 2 constitute the list of Martin and Ono of new forms given by eta-products/quotients.

math.NT↗
arXiv2009

On Gauss-Jacobi sums

This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.

math.NT↗
arXiv2009

Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve

We present a solvable two-dimensional piecewise linear chaotic map which arises from the duplication map of a certain tropical cubic curve. Its general solution is constructed by means of the ultradiscrete theta function. We show that the map is derived by the ultradiscretization of the duplication map associated with the Hesse cubic curve. We also show that it is possible to obtain the nontrivial ultradiscrete limit of the solution in spite of a problem known as "the minus-sign problem."

nlin.SI↗
arXiv2002

A variation of Euler's approach to values of the Riemann zeta function

An elementary method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical limit of this q-analogue exists and equals the value of the Riemann zeta.

math.QA↗