Odlyzko-Sch\"onhage algorithm in conductor aspect
Jeffrey Stopple · arXiv (Cornell University) · 2003
ABSTRACT. An algorithm is given to efficiently compute, for large discriminant, L-functions of characters on the class group of a complex quadratic field. This is an analog in conductor aspect of the Odlyzko-Schönhage algorithm to compute the Riemann zeta function. Examples are included for about 21000 L-functions with conductor near 10 7. The data shows good agreement with a symplectic random matrix model. 1. INTRODUCTION. In [6], Odlyzko and Schönhage developed an algorithm to compute the Riemann zeta function ζ(s) efficiently for values of s very high up in the critical strip. Their method depends on precomputation of Taylor series expansions of ζ(s) at regularly spaced points,