5 papers
On discriminants of minimal polynomials of the Ramanujan class invariants
Sarth Chavan
We study the discriminants of the minimal polynomials of the Ramanujan class invariants, which are defined for positive integers . The his…
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…
Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values
Parth Chavan, Sarth Chavan, Christophe Vignat +1
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its s…
Evaluation of multivariate integrals based on a duality identity for the Stieltjes transform
Sarth Chavan, Christophe Vignat
A detailed study of a double integral representation of the Catalan's constant allows us to identify a duality identity for the Stieltjes transform on which it is based. This duali…
An Elementary Proof of Ramanujan's Identity for Odd Zeta Values
Sarth Chavan
The main goal of this article is to present an elementary proof of Ramanujan's identity for odd zeta values. Our proof solely relies on a Mittag-Leffler type expansion for hyperbol…