5 papers
The joy of multisection: elementary approaches to Ramanujan's lacunary identities for Bernoulli numbers
Parth Chavan, Christophe Vignat
An identity by Ramanujan related to the multisection of Bernoulli numbers is revisited. Two alternative approaches are proposed, both relying on the multisection technique. A geome…
Counting Ideals in Numerical Semigroups
Parth Chavan
If is a numerical semigroup, let denote the number of ideals of with codimension and let denote the number of ideals of with conductor . We com…
Hurwitz Zeta Functions and Ramanujan's Identity for Odd Zeta Values
Parth Chavan
Inspired by a famous formula of Ramanujan for odd zeta values, we prove an analogous formula involving the Hurwitz zeta function. We introduce a new integral kernel related to the…
Hypergraph Fuss-Catalan Numbers
Parth Chavan, Andrew Lee, Karthik Seetharaman
The Catalan numbers are an extremely well-studied sequence of numbers that appear as the answer to many combinatorial problems. Two generalizations of these numbers that have…
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…