Brundaban Sahu

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It is known that the numbers which occur in Apéry’s proof of the irrationality of ζ(2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove supercongruences for a generalization of numbers which arise in Beukers’ and Zagier’s study of integral solutions of Apéry-like(More)
We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide tables of congruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apéry-like(More)
In [5], D. Lanphier used differential operators studied by Maass [6] to prove the above van der Pol identity (2). He also obtained several van der Pol-type identities using the Maass operators and thereby obtained new congruences for the Ramanujan’s tau-function. In [9], D. Niebur derived a formula for τ(n) similar to the classical ones of Ramanujan and van(More)
We prove two supercongruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide a table of supercongruences for numbers which appear in similar power series expansions and in the study of integral solutions of(More)
There are many interesting connections between differential operators and the theory of modular forms and many interesting results have been studied. In [10], R. A. Rankin gave a general description of the differential operators which send modular forms to modular forms. In [6], H. Cohen constructed bilinear operators and obtained elliptic modular form with(More)