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  Finiteness of irreducible holomorphic eta quotients of a given level

Bhattacharya, S. (2019). Finiteness of irreducible holomorphic eta quotients of a given level. The Ramanujan Journal, 48(2), 423-443. doi:10.1007/s11139-017-9982-6.

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Bhattacharya_Finiteness of irreducible holomorphic eta quotients of a given level_2019.pdf (Publisher version), 573KB
 
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Bhattacharya, Soumya1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: We show that for any positive integer N, there are only finitely many holomorphic eta quotients of level N, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier’s conjecture/Mersmann’s theorem which states that of any given weight, there are only finitely
many irreducible holomorphic eta quotients, none of which is an integral rescaling of another eta quotient. We construct such eta quotients for all cubefree levels. In particular, our construction demonstrates the existence of irreducible holomorphic eta quotients of arbitrarily large weights.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 742979
DOI: 10.1007/s11139-017-9982-6
URI: https://doi.org/10.1007/s11139-017-9982-6
Other: https://arxiv.org/abs/1602.02814
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Title: The Ramanujan Journal
  Abbreviation : Ramanujan J.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 48 (2) Sequence Number: - Start / End Page: 423 - 443 Identifier: -