The minimum of the levels of the proper factors of a holomorphic eta quotient

Soumya Bhattacharya*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The levels of the factors of a holomorphic eta quotient f are bounded above with respect to the weight and the level of f. Unfortunately, this bound remains implicit due to the ineffectiveness of Mersmann’s finiteness theorem. On the other hand, for checking whether f is irreducible, it is essential to know at least an explicit upper bound for the minimum mf among the levels of the proper factors of f. In the case where the level of f is a prime power, the least upper bound for mf has been recently determined via construction of a special factor. However, this construction does not generalize unconditionally to arbitrary levels. Here, we provide an explicit upper bound MN for the minimum of the levels of the proper factors of a holomorphic eta quotient f of level N.

Original languageEnglish
Article number33
JournalResearch in Mathematical Sciences
Volume8
Issue number2
DOIs
Publication statusPublished - Jun 2021

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)
  • Computational Mathematics
  • Applied Mathematics

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