5 citations · 9 across the 20 of their papers we have counts for
20 papers
Ramanujan-Shen's differential equations for Eisenstein series of level 2
Masato Kobayashi
Ramanujan (1916) and Shen (1999) discovered differential equations for classical Eisenstein series. Motivated by them, we derive new differential equations for Eisenstein series of…
Applications of Ramanujan's work on Eisenstein series
Masato Kobayashi
Ramanujan (1916) expressed quotients of certain q-series as polynomials of Eisenstein series of degree 2, 4, 6 and derived the famous Ramanujan's differential equations. We continu…
New recurrences for divisor sum functions and triangular numbers
Masato Kobayashi
Euler discovered recurrence for divisor sum functions as a consequence of the pentagonal numbers theorem. With similar idea and also motivated by Ewell's work in 1977, we prove new…
Values of zeta-one functions at positive even integers
Masato Kobayashi, Shunji Sasaki
Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of as an analogy of the Riemann zeta function. Then we comput…
From Basel Problem to multiple zeta values
Masato Kobayashi
We show many consequences of the proof of Basel problem by Boo Rim Choe (1987) to central binomial series, multiple zeta values and some other multiple sums. The main idea is to ev…
Integral Evaluation of Odd Euler Sums, Multiple -Value and Multiple Zeta Value
Sarth Chavan, Masato Kobayashi, Jorge Layja
We construct an analytic approach to evaluate odd Euler sums, multiple zeta value and multiple -value . Moreover, we also conjectur…
Integral representations for local dilogarithm and trilogarithm functions
Masato Kobayashi
We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apery, Ca…
Matrix representation of meet-irreducible discrete copulas
Masato Kobayashi
Following Aguiló-Suñer-Torrens (2008), Kolesárová-Mesiar-Mordelová-Sempi (2006) and Mayor-Suñer-Torrens (2005), we continue to develop a theory of matrix representation for discret…
New relations on zeta and functions
Masato Kobayashi
We prove new relations on zeta function at even arguments and Dirichlet function at odd. The key idea is to make use of the Taylor series and partial fraction decomposition of…
Möbius functions of higher rank and Dirichlet series
Masato Kobayashi
We introduce Möbius functions of higher rank, a new class of arithmetic functions so that the classical Möbius function is of rank 2. With this idea, we evaluate Dirichlet series o…
Integral representations for with the inverse sine function
Masato Kobayashi
We show four new integral representations for as a reformulation of Ewell (1990) and Yue-Williams (1993) with the inverse sine function and Wallis integral. As a consequence…
A new refinement of Euler numbers on counting alternating permutations
Masato Kobayashi
At a crossroads of calculus and combinatorics, the generating function of secant and tangent numbers (Euler numbers) provides enumeration of alternating permutations. In this artic…
Weighted counting of Bruhat paths by shifted -polynomials
Masato Kobayashi
We revisit -polynomials with introducing the new idea ``shifted -polynomials" (or Bruhat weight) for all Bruhat intervals in finite Coxeter groups. Then, we apply these polyn…
Construction of double coset system of a Coxeter group and its applications to Bruhat graphs
Masato Kobayashi
We develop combinatorics of parabolic double cosets in finite Coxeter groups as a follow-up of recent articles by Billey-Konvalinka-Petersen-Slofstra-Tenner and Petersen. (1) We co…
Weighted counting of inversions on alternating sign matrices
Masato Kobayashi
We extend the author's formula (2011) of weighted counting of inversions on permutations to the one on alternating sign matrices. The proof is based on the sequential construction…
A directed graph structure of alternating sign matrices
Masato Kobayashi
We introduce a new directed graph structure into the set of alternating sign matrices. This includes Bruhat graph (Bruhat order) of the symmetric groups as a subgraph (subposet). D…
Enumerative combinatorics on determinants and signed bigrassmannian polynomials
Masato Kobayashi
As an application of linear algebra for enumerative combinatorics, we introduce two new ideas, signed bigrassmannian polynomials and bigrassmannian determinant. First, a signed big…
Bruhat order and graph structures of lower intervals in Coxeter groups
Masato Kobayashi
We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we…
Inequalities on Bruhat graphs, R- and Kazhdan-Lusztig polynomials
Masato Kobayashi
From a combinatorial perspective, we establish three inequalities on coefficients of - and Kazhdan-Lusztig polynomials for crystallographic Coxeter groups: (1) Nonnegativity of…
Enumeration of bigrassmannian permutations below a permutation in Bruhat order
Masato Kobayashi
In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove for…