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Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56

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  • Ayşe Alaca

    (Carleton University)

Abstract

We explore the theta functions of nineteen positive-definite integral non-diagonal quaternary quadratic forms of discriminant 784 with levels 28 or 56. We express these theta functions in terms of Eisenstein series and cusp forms, which we then use to give explicit formulas for the representation number of a positive integer n by their corresponding non-diagonal quaternary quadratic forms. We also find the theta functions of the genera to which those non-diagonal quaternary quadratic forms belong. Finally, we express the theta function of each non-diagonal quadratic form in terms of the theta functions of certain diagonal quaternary quadratic forms and a cusp form.

Suggested Citation

  • Ayşe Alaca, 2023. "Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 595-607, June.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:2:d:10.1007_s13226-022-00278-x
    DOI: 10.1007/s13226-022-00278-x
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