#### 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.*

Google meet link: meet.google.com/pjg-chej-hnk

Done