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


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.


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

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