Theta Functions with Harmonic Coefficients over Number Fields
نویسندگان
چکیده
منابع مشابه
Jacobi Theta Functions over Number Fields
We use Jacobi theta functions to construct examples of Jacobi forms over number fields. We determine the behavior under modular transformations by regarding certain coefficients of the Jacobi theta functions as specializations of symplectic theta functions. In addition, we show how sums of those Jacobi theta functions appear as a single coefficient of a symplectic theta function. 2000 Mathemati...
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is a modular form of weight n/2 on Γ0(N), where N is the level of Q, i.e. NQ−1 is integral and NQ−1 has even diagonal entries. This was proved by Schoeneberg [5] for even n and by Pfetzer [3] for odd n. Shimura [6] uses the Poisson summation formula to generalize their results for arbitrary n and he also computes the theta multiplier explicitly. Stark [8] gives a different proof by converting θ...
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We report on a computation of congruent numbers, which subject to the Birch and Swinnerton-Dyer conjecture is an accurate list up to 10. The computation involves multiplying large theta series as per Tunnell (1983). The first method, which we describe in some detail, uses a multimodular disk based technique for multiplying polynomials out-of-core which minimises expensive disk access by keeping...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2002
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2758