A fast amortized algorithm for computing quadratic Dirichlet $L$-functions

TL;DR

This paper introduces an efficient amortized algorithm for computing quadratic Dirichlet L-functions across many characters, optimizing performance within specific conductor ranges.

Contribution

It presents a novel, nearly optimal algorithm for computing quadratic Dirichlet L-functions for multiple characters within a dyadic conductor window.

Findings

Algorithm achieves near-optimal performance up to logarithmic factors.

Efficiently handles large sets of quadratic characters.

Applicable within dyadic conductor ranges.

Abstract

An algorithm to compute Dirichlet $L$-functions for many quadratic characters is derived. The algorithm is optimal (up to logarithmic factors) provided that the conductors of the characters under consideration span a dyadic window.