TY - JOUR

T1 - The minimum of the levels of the proper factors of a holomorphic eta quotient

AU - Bhattacharya, Soumya

N1 - Funding Information:
This work was supported by the Austrian Science Fund (FWF), project F-5512.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85107048415&partnerID=8YFLogxK

U2 - 10.1007/s40687-021-00267-2

DO - 10.1007/s40687-021-00267-2

M3 - Article

AN - SCOPUS:85107048415

VL - 8

JO - Research in Mathematical Sciences

JF - Research in Mathematical Sciences

SN - 2522-0144

IS - 2

M1 - 33

ER -