BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20231105T010000 RDATE:20240310T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20281105T010000 RDATE:20290311T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20230919T170000 RDATE:20231105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20240310T030000 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20280312T030000 RDATE:20281105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:52381c3ffc10b7929c819fa4b9130c71 CATEGORIES:Experimental Mathematics Seminar CREATED:20240903T192218 SUMMARY: Searching for sequences: Irrationality beyond Apery LOCATION:https://rutgers.zoom.us/j/94346444480 password:The 20th Catalan number\, a lias (40)!/(20!*21!)\, alias 6564120420 DESCRIPTION:In 1978, Apery found a "miraculous" proof that zeta(3) is irrational, by fi nding an explicit pair of sequences of rational numbers a_n and b_n satisfy ing a recurrence relation so that their ratio a_n/b_n converged to zeta(3) "too quickly" for zeta(3) to be rational. Given another such pair of sequen ces, it is easy to verify experimentally whether or not the same "miracle" occurs. The problem is, it seems very hard in practice to find such miracul ous sequences whose ratio converges to other interesting Dirichlet L-values . In recent work with Vesselin Dimitrov and Yunqing Wang, we have found (mo re or less) a weaker condition on the sequences a_n and b_n which implies r ationality, and applied this to show that such numbers like\nL(2,chi_{-3}) = 1/1^2 - 1/2^2 + 1/4^2 - 1/5^2 + 1/7^2 - 1/8^2 + ,,,\nare irrational. The goal of this talk will be to sketch the basic idea, but the main point of t he talk will be to explain how to detect sequences which could at least *pl ausibly* establish irrationality of interesting constants, and also where o ne might try to look for them.\n X-ALT-DESC;FMTTYPE=text/html:

In 1978, Apery found a "miraculous" proof that zeta(3) is irrational, by finding an explicit pair of sequences of rational numbers a_ n and b_n satisfying a recurrence relation so that their ratio a_n/b_n conv erged to zeta(3) "too quickly" for zeta(3) to be rational. Given another su ch pair of sequences, it is easy to verify experimentally whether or not th e same "miracle" occurs. The problem is, it seems very hard in practice to find such miraculous sequences whose ratio converges to other interesting D irichlet L-values. In recent work with Vesselin Dimitrov and Yunqing Wang, we have found (more or less) a weaker condition on the sequences a_n and b_ n which implies rationality, and applied this to show that such numbers lik e

L(2,chi_{-3}) = 1/1^2 - 1/2^2 + 1/4^2 - 1/5^2 + 1/7^2 - 1/8^2 + ,,,

are irrational. The goal of this talk wi ll be to sketch the basic idea, but the main point of the talk will be to e xplain how to detect sequences which could at least *plausibly* establish i rrationality of interesting constants, and also where one might try to look for them.

CONTACT:Frank Calegari, University of Chicago DTSTAMP:20260827T043220 DTSTART;TZID=America/New_York:20240919T170000 DTEND;TZID=America/New_York:20240919T180000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR