#### Filter Results:

- Full text PDF available (10)

#### Publication Year

2006

2014

- This year (0)
- Last 5 years (3)
- Last 10 years (10)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

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)

Abstract. Following Rankin’s method, D. Zagier computed the n-th Rankin-Cohen bracket of a modular form g of weight k1 with the Eisenstein series of weight k2 and then computed the inner product of this Rankin-Cohen bracket with a cusp form f of weight k = k1 + k2 + 2n and showed that this inner product gives, upto a constant, the special value of the… (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)

Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier’s seven “sporadic” solutions to second order Apéry-like differential equations.

We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.

- Brundaban Sahu
- 2008

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)

- Brundaban Sahu
- 2008

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)

It is known that the numbers which occur in Apéry’s proof of the irrationality of ζ(2) have many interesting congruences properties while the associated generating function satisfies a second order differential equation. We prove congruences for numbers which arise in Beukers’ and Zagier’s study of integral solutions of Apéry-like differential equations.

- B. Ramakrishnan, Brundaban Sahu
- Int. J. Math. Mathematical Sciences
- 2006

Using the relationship between Jacobi forms of half-integral weight and vector valued modular forms, we obtain the number of components which determine the given Jacobi form of index p, p or pq, where p and q are odd primes.