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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)

- S. Gun, Florian Luca, P. Rath, B. Sahu
- 2006

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 con-jectural supercongruence for numbers which are coefficients in one of Zagier's seven " sporadic " solutions to second order Apéry-like differential equations.

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)

Following Rankin's method, D. Zagier computed the n-th Rankin-Cohen bracket of a modular form g of weight k 1 with the Eisenstein series of weight k 2 and then computed the inner product of this Rankin-Cohen bracket with a cusp form f of weight k = k 1 + k 2 + 2n and showed that this inner product gives, upto a constant, the special value of the… (More)

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 2 or pq, where p and q are odd primes.

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 supercon-gruences.

The genetic diversity of five feral populations of Asian Sea bass, Lates calcarifer collected from five isolated locations in India viz., Paradeep, Chilka lake, Kakinada, Chennai and Mumbai was studied using randomly amplified polymorphic DNA. Out of 20 primers screened, 5 decamer random primers amplified a total of 373 DNA bands of which 137 bands were… (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)

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.