IMSc Webinar

Lacunary eta-quotients and distribution of certain partition functions

Rupam Barman

IIT Guwahati

An integral power series is called lacunary modulo M if almost all of its coefficients are divisible by M. Motivated by the parity problem for the partition function, Gordon and Ono studied the generating function for $\ell$-regular partition and determined conditions for when these functions are lacunary modulo powers of primes. In this talk, we study certain lacunary eta-quotients and generalised eta-quotients modulo powers of primes, and improve the result of Gordon and Ono by removing a strong condition on primes dividing $\ell$. We also discuss distribution of certain other partition functions.
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