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EISENSTEIN SERIES TO THE TREDECIC BASE

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  27 June 2014

SHAUN COOPER  and
DONGXI YE
SHAUN COOPER
Affiliation:
Institute of Natural and Mathematical Sciences, Massey University-Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand email [email protected]
DONGXI YE*
Affiliation:
Institute of Natural and Mathematical Sciences, Massey University-Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand email [email protected]
*
✉[email protected]
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Abstract

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We employ a modular method to establish the new result that two types of Eisenstein series to the tredecic base may be parametrised in terms of the eta quotients ${\it\eta}^{13}({\it\tau})/{\it\eta}(13{\it\tau})$ and ${\it\eta}^{2}(13{\it\tau})/{\it\eta}^{2}({\it\tau})$. The method can also be used to give short and simple proofs for the analogous cubic, quintic and septic theories.

Keywords

Eisenstein seriesDedekind’s eta function

MSC classification

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F20: Dedekind eta function, Dedekind sums 11F03: Modular and automorphic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 19 - 28
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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