Computing Jacobi’s theta in quasi-linear time
نویسندگان
چکیده
منابع مشابه
Computing Theta functions in quasi-linear time in genus two and above
We outline an algorithm to compute θ(z, τ) in genus two in quasi-linear time, borrowing ideas from the algorithm for theta constants and the one for θ(z, τ) in genus one. Our implementation shows a large speed-up for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus g.
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Jacobi’s θ function has numerous applications in mathematics and computer science; a naive algorithm allows the computation of θ(z, τ), for z, τ verifying certain conditions, with precision P in O(M(P ) √ P ) bit operations, where M(P ) denotes the number of operations needed to multiply two complex P -bit numbers. We generalize an algorithm which computes specific values of the θ function (the...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2017
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3245