BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ahmed El-Guindy (Cairo University) DTSTART:20241024T133000Z DTEND:20241024T143000Z DTSTAMP:20260422T102551Z UID:FGC-IPM/48 DESCRIPTION:Title: Some l-adic properties of modular forms with quadratic nebentypus and l-r egular partition congruences\nby Ahmed El-Guindy (Cairo University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this talk\, we discuss a framework for studying l-regular partitions by defining a seq uence of\nmodular forms of level l and quadratic character which encode th e l-adic behavior of the so-called l-regular\npartitions. We show that thi s sequence is congruent modulo increasing powers of l to level 1 modular f orms of\nincreasing weights. We then prove that certain modules generated by our sequence are isomorphic to certain\nsubspaces of level 1 cusp forms of weight independent of the power of l\, leading to a uniform bound on t he\nranks of those modules and consequently to l-adic relations between l- regular partition values. This\ngeneralizes earlier work of Folsom\, Kent and Ono on the partition function\, where the relevant forms had no\nneben typus\, and is joint work with Mostafa Ghazy.\n\npassword is 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/48/ END:VEVENT END:VCALENDAR