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math.NT2020
Computing isolated coefficients of the -function
Fredrik Johansson
We consider the problem of efficiently computing isolated coefficients in the Fourier series of the elliptic modular function . We show that a hybrid numerical-modular…
math.NT2016
Short addition sequences for theta functions
Andreas Enge, William Hart, Fredrik Johansson
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…
math.NT2012★ 32 cited
Efficient implementation of the Hardy-Ramanujan-Rademacher formula
Fredrik Johansson
We describe how the Hardy-Ramanujan-Rademacher formula can be implemented to allow the partition function to be computed with softly optimal complexity and…