Zeros of Modular Forms

Specialeforsvar ved Mads Friis Frand-Madsen

Titel: Zeros of Modular Forms

Abstract: The notion of modular forms is introduced and we give some elementary results on the zeros of modular forms, in particular of Eisenstein series, before turning to Hecke operators and a proof of self-adjointness with respect to the Petersson inner product. Moving on we give several characterizations of subharmonic functions in order to establish a compactness property and Hartog's Lemma, which we apply as in Rudnick's proof of asymptotic equidistribution of zeros of cusp forms. Towards the end we briefly discuss Rudnick's result in conjunction with a recent advance in proving asymptotic equidistribution of mass Hecke eigencuspsforms.

Vejleder: Morten S. Risager
Censor: Simon Kristensen