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Short addition sequences for theta functions

Enge , Andreas; Hart , William; Johansson , Fredrik (2018)
Projects: EC | ANTICS (278537)
International audience; The main step in numerical evaluation of classical Sl2 (Z) modular forms and elliptic functions is to compute the sum of the first N nonzero terms in the sparse q-series belonging to the Dedekind eta function or the Jacobi theta constants. We construct short addition sequences to perform this task using N + o(N) multiplications. Our constructions rely on the representability of specific quadratic progressions of integers as sums of smaller numbers of the same kind. For...
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