Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 30, 2018 - 16:00 to 17:00

Location:

Bexell 102

Local Speaker:

Abstract:

We show that a sufficient condition of Newman for an eta-quotient to be modular over the group Gamma_0(N) is in fact necessary for modularity over Gamma_1(N) when N is coprime to 6. Using this, we then give necessary and sufficient conditions for existence of eta-quotients in spaces of holomorphic modular forms over Gamma_1(N) when N is either a prime coprime to 6 or a product of two distinct such primes. We also give criteria for existence of weakly holomorphic eta-quotients for all squarefree N coprime to 6. Finally, we make use of the modularity theorem to give examples of classes of elliptic curves which correspond to linear combinations of eta-quotients.