5 citations · 9 across the 20 of their papers we have counts for
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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…
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…