{"id":4892,"date":"2016-05-09T21:46:23","date_gmt":"2016-05-09T19:46:23","guid":{"rendered":"https:\/\/wpethzprd.ethz.ch\/kowalski\/?p=4892"},"modified":"2024-02-20T13:40:32","modified_gmt":"2024-02-20T11:40:32","slug":"l-functions-database","status":"publish","type":"post","link":"https:\/\/blogs.ethz.ch\/kowalski\/2016\/05\/09\/l-functions-database\/","title":{"rendered":"L-functions database!"},"content":{"rendered":"<p>People studying <a href=\"http:\/\/gdz.sub.uni-goettingen.de\/dms\/load\/img\/?PID=GDZPPN002110717\">automorphic forms<\/a>, <a href=\"http:\/\/sunsite.ubc.ca\/DigitalMathArchive\/Langlands\/pdf\/jl-ps.pdf\">automorphic representations<\/a>, <a href=\"http:\/\/numdam.org\/numdam-bin\/fitem?id=ASNSP_1976_4_3_4_623_0\">number fields<\/a>, <a href=\"https:\/\/www.math.ias.edu\/~anindya\/fermat.pdf\">diophantine equations<\/a>, <a href=\"http:\/\/www.ams.org\/journals\/bull\/1999-36-01\/S0273-0979-99-00766-1\/\">function fields<\/a>, <a href=\"https:\/\/people.math.ethz.ch\/~kowalski\/relations-roots.pdf\">algebraic curves<\/a>, <a href=\"http:\/\/math.stanford.edu\/~akshay\/research\/linnik.pdf\">equidistribution<\/a> and many other arithmetic objects (<i>j&#8217;en passe, et des meilleurs<\/i>), often end up with some &#8220;L-function&#8221; to deal with &#8212; indeed, probably equally often, with a <a href=\"http:\/\/tan.epfl.ch\/files\/content\/sites\/tan\/files\/PhMICHELfiles\/Parkcitylectures.pdf\">whole family of them<\/a>, sometimes not so well-behaved&#8230;  These objects are <a href=\"http:\/\/arxiv.org\/pdf\/math\/0005300v1.pdf\">fascinating<\/a>, <a href=\"http:\/\/gdz.sub.uni-goettingen.de\/dms\/load\/img\/?PID=GDZPPN00209326X\">mystifying<\/a>, <a href=\"http:\/\/publications.ias.edu\/sites\/default\/files\/Perspectives%20on%20the%20Analytic%20Theory%20of%20L-functions.pdf\">exhilarating<\/a>, <a href=\"https:\/\/blogs.ethz.ch\/kowalski\/2016\/04\/09\/bagchis-theorem\/\">random<a> and possibly <a href=\"http:\/\/www.ams.org\/notices\/200907\/rtx090700817p.pdf\">spooky<\/a>.  Where they really come from is still a mystery, even with buzzwords aplenty ringing around our ears.  But one remarkable thing was already known to Euler and to Riemann: one can compute with L-functions.  One impressive research project has been building, for quite a few years, a very sophisticated website presenting enormous amounts of data about L-functions of many kinds.  The <a href=\"http:\/\/www.lmfdb.org\/\">L-functions Database<\/a> is now out of its beta status: go see it, and have a look at the <a href=\"http:\/\/beta.lmfdb.org\/editorial-board\">list of editors<\/a> to see who should be thanked for this amazing work!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>People studying automorphic forms, automorphic representations, number fields, diophantine equations, function fields, algebraic curves, equidistribution and many other arithmetic objects (j&#8217;en passe, et des meilleurs), often end up with some &#8220;L-function&#8221; to deal with &#8212; indeed, probably equally often, with a whole family of them, sometimes not so well-behaved&#8230; These objects are fascinating, mystifying, exhilarating, &hellip; <a href=\"https:\/\/blogs.ethz.ch\/kowalski\/2016\/05\/09\/l-functions-database\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">L-functions database!<\/span><\/a><\/p>\n","protected":false},"author":625,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[904,2,624],"tags":[],"class_list":["post-4892","post","type-post","status-publish","format-standard","hentry","category-computers","category-blogroll","category-science"],"_links":{"self":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/4892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/users\/625"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/comments?post=4892"}],"version-history":[{"count":0,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/4892\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/media?parent=4892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/categories?post=4892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/tags?post=4892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}