Finiteness results on eta quotients and some applications

14 dicembre 2015
14 dicembre 2015
Contatti: 
Staff Dipartimento di Matematica

Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari

Ore 11:30

Relatore:

  • Soumya Bhattacharya(Post Doc CIRM Trento)

Abstract
We show that for any positive integer N, there are only finitely many irreducible holomorphic eta quotients of level N. This is an analog of a conjecture of Zagier which says that for any positive integer k, there are only finitely many irreducible holomorphic eta quotients of weight k/2 which are not integral rescalings of some other eta quotients. This conjecture was established in 1991 by Mersmann.
We shall show that both of the above results have their applications in solving the fundamental problem of constructing an explicit upper bound with respect to N for the levels of the factors of a holomorphic eta quotient of level N.

Referente: Marco Andreatta