#l-functions

Foundations of Computational Mathematics - The L-Functions and Modular Forms Database Project #mathematics #database #lfunctions #modularforms

From the journal, Foundations of Computational Mathematics, comes a paper on The L-Functions and Modular Forms Database Project. This paper is free to read (link) through September 2019.

Abstract

The Langlands Programme, formulated by Robert Langlands in the 1960s and since much developed and refined, is a web of interrelated theory and conjectures concerning many objects in number…

…I rejoice that a major new database was launched today. It’s not in my area, so I won’t be using it, but I am nevertheless very excited that it exists. It is called the L-functions and modular forms database. The thinking behind the site is that lots of number theorists have privately done lots of difficult calculations concerning L-functions, modular forms, and related objects. Presumably up to now there has been a great deal of duplication, because by no means all these calculations make it into papers, and even if they do it may be hard to find the right paper. But now there is a big database of these objects, with a large amount of information about each one, as well as a great big graph of connections between them. I will be very curious to know whether it speeds up research in number theory: I hope it will become a completely standard tool in the area and inspire people in other areas to create databases of their own.

Analytic Class Number Formula http://wp.me/sN6Ai-acnf

I proved this identity in a post several years ago on Number Theory and Pi. It turns out that this is a special case of a more general identity called the analytic class number formula (ACNF) that evaluates an analytic quantity–a L-function at 1, –in terms of algebraic information about an extension of . I have just added a chapter on the ACNF in the open-source number theory text(currently…