Section: New Results

Complex $L$-functions and certified arithmetic

Participants : Bill Allombert, Karim Belabas, Henri Cohen, Fredrik Johansson.

Fredrik Johansson's paper [23] has been published and presented at the 22nd IEEE Symposium on Computer Arithmetic (ARITH22), Lyon, France. This paper describes a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. Compared to the MPFR library, it achieves a maximum speedup ranging from a factor 3 for cos to 30 for atan.

Bill Allombert, Karim Belabas, Henri Cohen and Pascal Molin (Paris 7) have implemented a new framework in Pari/Gp to compute and manipulate complex $L$-functions and the associated $\vartheta$ and $\Lambda$ functions, exporting 25 new functions to the Gp computer algebra system.