BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Didier Lesesvre (U of Lille) DTSTART:20241122T203000Z DTEND:20241122T213000Z DTSTAMP:20260423T010133Z UID:NT-UBC/5 DESCRIPTION:Title: R elation between low-lying zeros and central values\nby Didier Lesesvre (U of Lille) as part of UBC Number theory seminar\n\nLecture held in ESB4 133.\n\nAbstract\nIn practice\, L-functions appear as generating functions \nencapsulating information about various objects\, such as Galois\nrepres entations\, elliptic curves\, arithmetic functions\, modular forms\,\nMaas s forms\, etc. Studying L-functions is therefore of utmost importance\nin number theory at large. Two of their attached data carry critical\ninforma tion: their zeros\, which govern the distributional behavior of\nunderlyin g objects\; and their central values\, which are related to\ninvariants su ch as the class number of a field extension. We discuss a\nconnection betw een low-lying zeros and central values of L-functions\, in\nparticular sho wing that results about the distribution of low-lying\nzeros (towards the density conjecture of Katz-Sarnak) implies results\nabout the distribution of the central values (towards the normal\ndistribution conjecture of Kea ting-Snaith). Even though we discuss this\nprinciple in general\, we insta nciate it in the case of modular forms in\nthe level aspect to give a stat ement and explain the arguments of the proof\n LOCATION:https://researchseminars.org/talk/NT-UBC/5/ END:VEVENT END:VCALENDAR