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Hideki Murahara

Publications and source records attributed to Hideki Murahara.

45 records · Page 3Linked to original sources
arXiv2018

A note on derivation relations for multiple zeta values and finite multiple zeta values

The derivation relation is a well known relation among multiple zeta values, which was first obtained by Ihara, Kaneko and Zagier. The analogous formula for finite multiple zeta values, which we call the derivation relation for finite multiple zeta values, was conjectured by the third author and proved by the second author. In this paper, we show these two kinds of derivation relations are respectively equivalent to the Ohno type relations for multiple zeta values and finite multiple zeta values. We also reprove these derivation relations in several different ways.

math.NT↗
arXiv2018

Weighted sum formula for multiple harmonic sums modulo primes

In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes difference equations for the generating series of multiple harmonic sums. We also conjecture several weighted sum formulas of similar flavor for finite multiple zeta values.

math.NT↗
arXiv2018

A cyclic analogue of multiple zeta values

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of $\mathbb{Q}$-linear relations among CMZVs. One of them is a generalization of the cyclic sum formula for multiple zeta-star values. We also give an alternative proof of the derivation relation for multiple zeta values.

math.NT↗
arXiv2018

Restricted sum formula for finite and symmetric multiple zeta values

The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to a rational multiple of the analogue of the Riemann zeta value. We prove that the result remains true if we further demand that the component should be more than two or that another component should also be more than one.

math.NT↗
arXiv2016

A Note on Finite Real Multiple Zeta Values

We prove three theorems on finite real multiple zeta values: the symmetric formula, the sum formula and the height-one duality theorem. These are analogues of their counterparts on finite multiple zeta values.

math.NT↗