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Theta series associated with certain positive definite binary quadratic forms

Volume 169 / 2015

Heng Huat Chan, Pee Choon Toh Acta Arithmetica 169 (2015), 331-356 MSC: Primary 11E16; Secondary 11R29. DOI: 10.4064/aa169-4-3

Abstract

Recently, P. C. Toh derived identities expressing theta series associated with fundamental idoneal discriminants in terms of generalized Lambert series. His method depends on the fact that the ring of integers of a number field is a Dedekind domain, and is not applicable to theta series associated with non-fundamental idoneal discriminants. The aim of this article is to devise methods for determining the generalized Lambert series representations of theta series associated with non-fundamental idoneal discriminants.

Authors

  • Heng Huat ChanDepartment of Mathematics
    National University of Singapore
    10 Lower Kent Ridge Road
    Singapore 119076
    e-mail
  • Pee Choon TohMathematics & Mathematics Education
    National Institute of Education
    Nanyang Technological University
    1 Nanyang Walk
    Singapore 637616
    e-mail

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