FLINT3.7.0-dev
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DedekindSum, DedekindEtaEpsilon, JacobiThetaEpsilon, JacobiThetaPermutation

Synopsis#include <flint/fexpr_builtin.h>
DedekindSum
DedekindEtaEpsilon
JacobiThetaEpsilon
JacobiThetaPermutation

Quantities in modular transformation formulas: the Dedekind sum DedekindSum(h, k) (s(h,k)s(h, k)), the root of unity DedekindEtaEpsilon(a, b, c, d) (ε(a,b,c,d)\varepsilon(a, b, c, d)) in the transformation of η\eta under a matrix (abcd)\left(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\right), and the root of unity JacobiThetaEpsilon(j, a, b, c, d) (εj ⁣(a,b,c,d)\varepsilon_{j}\!\left(a, b, c, d\right)) and index permutation JacobiThetaPermutation(j, a, b, c, d) (Sj ⁣(a,b,c,d)S_{j}\!\left(a, b, c, d\right)) in the transformation of θj\theta_j.

Cite this page

The FLINT team, “DedekindSum, DedekindEtaEpsilon, JacobiThetaEpsilon, JacobiThetaPermutation (fexpr_builtin.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fexpr_builtin/DedekindSum.html (generated 2026-11-02).