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The L-functions and modular forms database project

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Cremona, J. E. (2016) The L-functions and modular forms database project. Foundations of Computational Mathematics . doi:10.1007/s10208-016-9306-z

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Official URL: http://dx.doi.org/10.1007/s10208-016-9306-z

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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 theory, their interconnections, and connections to other fields. At the heart of the Langlands Programme is the concept of an L-function. The most famous L-function is the Riemann zeta function, and as well as being ubiquitous in number theory itself, L-functions have applications in mathematical physics and cryptography. Two of the seven Clay Mathematics Million Dollar Millennium Problems, the Riemann Hypothesis and the Birch and Swinnerton-Dyer Conjecture, deal with their properties. Many different mathematical objects are connected in various ways to L-functions, but the study of those objects is highly specialized, and most mathematicians have only a vague idea of the objects outside their specialty and how everything is related. Helping mathematicians to understand these connections was the motivation for the L-functions and Modular Forms Database (LMFDB) project. Its mission is to chart the landscape of L-functions and modular forms in a systematic, comprehensive, and concrete fashion. This involves developing their theory, creating and improving algorithms for computing and classifying them, and hence discovering new properties of these functions, and testing fundamental conjectures. In the lecture I gave a very brief introduction to L-functions for non-experts and explained and demonstrated how the large collection of data in the LMFDB is organized and displayed, showing the interrelations between linked objects, through our website www.lmfdb.org. I also showed how this has been created by a worldwide open-source collaboration, which we hope may become a model for others.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): L-functions, Number theory, Forms, Modular, Forms (Mathematics)
Journal or Publication Title: Foundations of Computational Mathematics
Publisher: Springer
ISSN: 1615-3375
Official Date: 16 February 2016
Dates:
DateEvent
16 February 2016Available
11 January 2016Accepted
24 September 2015Submitted
Date of first compliant deposit: 1 February 2016
DOI: 10.1007/s10208-016-9306-z
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: National Science Foundation (U.S.) (NSF), Engineering and Physical Sciences Research Council (EPSRC)
Grant number: DMS:0757627 (NSF), EP/K034383/1 (EPSRC)
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