7 papers · 1 filter
An explicit parity theorem for multiple polylogarithms
Ryota Umezawa
In 2017, E. Panzer proved the parity theorem for multiple polylogarithms. While his proof is simple and constructive, it does not yield a general explicit formula. Inspired by M. H…
Relations of multiple -values involving the total numbers of certain permutations
Ryota Umezawa
Kaneko and Tsumura proved a relation of multiple -values involving Entringer numbers counting the total number of down-up permutations starting with a fixed value. In th…
Counting relatively prime pairs of palindromes
Hirotaka Kobayashi, Yuta Suzuki, Ryota Umezawa
For a given base , a positive integer is called a palindrome if its base expansion reads the same backwards as forwards. In this paper, we give an asymptotic formula for…
Multiple -values and iterated log-tangent integrals
Ryota Umezawa
Multiple -values, a variant of multiple zeta values of level two, were introduced and studied by Kaneko and Tsumura. This paper will introduce iterated log-tangent integrals and…
Evaluation of iterated log-sine integrals in terms of multiple polylogarithms
Ryota Umezawa
It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polyl…
Multiple zeta values and iterated log-sine integrals
Ryota Umezawa
We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-s…
On an analog of the Arakawa-Kaneko zeta function and relations of some multiple zeta values
Ryota Umezawa
T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an ana…