18 citations · 40 across the 16 of their papers we have counts for
17 papers
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…
-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…
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…
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…
Generating functions for Ohno type sums of finite and symmetric multiple zeta-star values
Minoru Hirose, Hideki Murahara, Shingo Saito
Ohno's relation states that a certain sum, which we call an Ohno type sum, of multiple zeta values remains unchanged if we replace the base index by its dual index. In view of Oyam…
Analogues of the Aoki-Ohno and Le-Murakami relations for finite multiple zeta values
Masanobu Kaneko, Kojiro Oyama, Shingo Saito
We establish finite analogues of the identities known as the Aoki-Ohno relation and the Le-Murakami relation in the theory of multiple zeta values. We use an explicit form of a gen…
Weighted sum formula for multiple harmonic sums modulo primes
Minoru Hirose, Hideki Murahara, Shingo Saito
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 d…
Polynomial generalization of the regularization theorem for multiple zeta values
Minoru Hirose, Hideki Murahara, Shingo Saito
Ihara, Kaneko, and Zagier defined two regularizations of multiple zeta values and proved the regularization theorem that describes the relation between those regularizations. We sh…
Ohno type relations for classical and finite multiple zeta-star values
Minoru Hirose, Kohtaro Imatomi, Hideki Murahara +1
Ohno's relation is a generalization of both the sum formula and the duality formula for multiple zeta values. Oyama gave a similar relation for finite multiple zeta values, defined…
Restricted sum formula for finite and symmetric multiple zeta values
Hideki Murahara, Shingo Saito
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 componen…
Sum formula for finite multiple zeta values
Shingo Saito, Noriko Wakabayashi
The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite m…
Bowman-Bradley type theorem for finite multiple zeta values
Shingo Saito, Noriko Wakabayashi
The multiple zeta values are multivariate generalizations of the values of the Riemann zeta function at positive integers. The Bowman-Bradley theorem asserts that the multiple zeta…
Knot points of typical continuous functions
David Preiss, Shingo Saito
It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strong…
Combinatorial remarks on the cyclic sum formula for multiple zeta values
Shingo Saito, Tatsushi Tanaka, Noriko Wakabayashi
The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the c…
The Bowman-Bradley theorem for multiple zeta-star values
Hiroki Kondo, Shingo Saito, Tatsushi Tanaka
The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of twos between 3,1,...,3,1 add up to a rational multiple of…
Continuity Points of Typical Bounded Functions
Shingo Saito
Kostyrko and Salat showed that if a linear space of bounded functions has an element that is discontinuous almost everywhere, then a typical element in the space is discontinuous a…
Residuality of Families of F-sigma Sets
Shingo Saito
We prove that two natural definitions of residuality of families of F-sigma sets are equivalent. We make use of the Banach-Mazur game in the proof.