8 citations · 35 across the 37 of their papers we have counts for
43 papers
On the uniform distribution modulo of zeros and -points of zeta functions
Hideki Murahara, Tomokazu Onozuka
Fujii gave five sufficient conditions for the uniform distribution modulo of the sequence , where runs over the imaginary parts of the non-trivial zeros of th…
A note on order estimates of the -analogue of the Riemann zeta function
Hideki Murahara, Tomokazu Onozuka
At the first step of studying order estimates for the -analogue of the Riemann zeta function, we estimate bounds for it on vertical lines for a fixed parameter .
On the mean values of the Barnes multiple zeta function
Takashi Miyagawa, Hideki Murahara
The asymptotic behavior of the mean values of multiple zeta functions is of significant interest due to its close connection with the Riemann zeta function. In this paper, we estab…
Ohno relation for regularized refined symmetric multiple zeta values
Minoru Hirose, Hideki Murahara, Shingo Saito
The Ohno relation is one of the most celebrated results in the theory of multiple zeta values, which are iterated integrals from to . In a previous paper, the authors genera…
Asymptotic coefficients of multiple zeta functions at the origin and generalized Gregory coefficients
Toshiki Matsusaka, Hideki Murahara, Tomokazu Onozuka
Due to their singularities, multiple zeta functions behave sensitively at non-positive integer points. In this article, we focus on the asymptotic behavior at the origin $(0,\dots,…
Multiple zeta-star values for indices of infinite length
Minoru Hirose, Hideki Murahara, Tomokazu Onozuka
In this paper, we consider infinite-length versions of multiple zeta-star values. We give several explicit formulas for the infinite-length versions of multiple zeta-star values. W…
On the asymptotic behavior of the double zeta function for large negative indices
Minoru Hirose, Hideki Murahara, Tomokazu Onozuka
In this paper, we investigate an asymptotic behavior of the double zeta function of Euler-Zagier type for indices with large negative real parts.
Interpolated polynomial multiple zeta values of fixed weight, depth, and height
Minoru Hirose, Hideki Murahara, Shingo Saito
We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetr…
Rooted tree maps for multiple -values from a perspective of harmonic algebras
Hideki Murahara, Tatsushi Tanaka, Noriko Wakabayashi
In this paper, we show the image of rooted tree maps themselves forms a subspace of the kernel of the evaluation map of multiple -values. For its proof, we define the diamond pr…
Integral expressions for Schur multiple zeta values
Minoru Hirose, Hideki Murahara, Tomokazu Onozuka
Nakasuji, Phuksuwan, and Yamasaki defined the Schur multiple zeta values and gave iterated integral expressions of the Schur multiple zeta values of the ribbon type. This paper gen…
-adic symmetric multiple zeta values for indices in which and appear alternately
Minoru Hirose, Hideki Murahara, Shingo Saito
We consider the symmetric multiple zeta values in without modulo reduction for indices in which and appear alternately. We investigate those values th…
Asymptotic behavior of the Hurwitz-Lerch multiple zeta function at non-positive integer points
Hideki Murahara, Tomokazu Onozuka
We give a result on the asymptotic behavior of the Hurwitz-Lerch multiple zeta functions near non-positive integer points by using the Apostol-Bernoulli polynomials. From this resu…
On the linear relations among parametrized multiple series
Minoru Hirose, Hideki Murahara, Tomokazu Onozuka
Parametrized multiple series are generalizations of the multiple zeta values introduced by Igarashi. In this work, we completely determine all the linear relations among these para…
Ohno relation for regularized multiple zeta values
Minoru Hirose, Hideki Murahara, Shingo Saito
The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined for indices, is invariant under taking duals. In this paper, we generalize t…
Ohno-type relation for interpolated multiple zeta values
Minoru Hirose, Hideki Murahara, Masataka Ono
We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given.…
A note on Ohno sums for multiple zeta values
Hideki Murahara
The Ohno relation is a well-known relation among multiple zeta values. Hirose, Onozuka, Sato, and the author investigated the sum related to the Ohno relation and presented two typ…
Connectors of the Ohno relation for parametrized multiple zeta series
Hideki Murahara, Tomokazu Onozuka
The Ohno relation is a well known relation in the theory of multiple zeta values. Recently, Seki and Yamamoto introduced a connector method and gave its succinct proof. On the othe…
Generating functions for sums of polynomial multiple zeta values
Minoru Hirose, Hideki Murahara, Shingo Saito
The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manne…
Algebraic aspects of rooted tree maps
Hideki Murahara, Tatsushi Tanaka
Based on the Connes--Kreimer Hopf algebra of rooted trees, the rooted tree maps are defined as linear maps on noncommutative polynomial algebra in two indeterminates. It is known t…
On a basis for Euler-Zagier double zeta functions with non-positive components
Hideki Murahara, Takashi Nakamura
For a non-negative integer , let , where the right-hand side is the vector space spanned by the Euler-Zagier double z…
On a generalization of the cyclic sum formula for finite multiple zeta and zeta-star values
Hideki Murahara
The cyclic sum formulas for multiple zeta and zeta-star values were respectively proved by Hoffman and Ohno, and Ohno and Wakabayashi. Kawasaki and Oyama obtained an analogous form…
Cyclic relation for multiple zeta functions
Hideki Murahara, Tomokazu Onozuka
The cyclic relation obtained in a study by Hirose, Murakami, and the first-named author, is a wide class of relations, which includes the well-known cyclic sum formula for multiple…
On variants of symmetric multiple zeta-star values and the cyclic sum formula
Minoru Hirose, Hideki Murahara, Masataka Ono
The -adic symmetric multiple zeta values were defined Jarossay, which have been studied as a real analogue of -adic finite multiple zeta values. In this paper, w…
On the -points of symmetric sum of multiple zeta function
Hideki Murahara, Tomokazu Onozuka
In this paper, we present some results on the -points of the symmetric sum of the Euler-Zagier multiple zeta function. Our first three results are for the -points free region…