Congruent Number Theta Coefficients to 1012
نویسندگان
چکیده
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 data truncated. The second technique uses “Bailey’s four-step” Fast Fourier method in combination with compression of the data to disk in intermediate stages.
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