EISENSTEIN SERIES TO THE TREDECIC BASE

Publisher： Cambridge University Press

E-ISSN： 1755-1633|91|1|19-28

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.91, Iss.1, 2015-02, pp. : 19-28

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Abstract

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.

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