[Turkmath:6668] Fwd: FGC-HRI-IPM Number Theory Seminars

[Özlem Ejder]

Merhaba,

Bu haftaki Feza Gürsey (FGC-IPM-HRI) sayılar teorisi seminerinin
detaylarını altta bulabilirsiniz.

Sevgiler,

*Date and Time: *Thursday, October 24, 5pm
*Zoom link:* https://kocun.zoom.us/j/99715471656
*Meeting ID: *997 1547 1656
*passcode:* 848084

*Speaker*: Ahmad El-Guindy, Cairo University
*Title: *Some l-adic properties of modular forms with quadratic nebentypus
and l-regular partition congruences
*Abstract:* In this talk, we discuss a framework for studying l-regular
partitions by defining a sequence of modular forms of level l and quadratic
character which encode the l-adic behavior of the so-called l-regular
partitions. We show that this sequence is congruent modulo increasing
powers of l to level 1 modular forms of increasing weights. We then prove
that certain modules generated by our sequence are isomorphic to certain
subspaces of level 1 cusp forms of weight independent of the power of l,
leading to a uniform bound on the ranks of those modules and consequently
to l-adic relations between l-regular partition values. This generalizes
earlier work of Folsom, Kent and Ono on the partition function, where the
relevant forms had no nebentypus, and is joint work with Mostafa Ghazy.



---------- Forwarded message ---------
From: FGC-HRI-IPM Number Theory Seminars <
fgc-hri-ipm-numbertheory at googlegroups.com>
Date: Sat, Oct 19, 2024 at 10:04 AM
Subject: FGC-HRI-IPM Number Theory Seminars
To: FGC-HRI-IPM Number Theory Seminars <
fgc-hri-ipm-numbertheory at googlegroups.com>


Dear all,

Our next talk in the FGC-HRI-IPM number theory seminars is Thursday Oct 24.
Please note the unusual date and find the details of the talk below.

*Speaker*: Ahmad El-Guindy, Cairo University
*Title: *Some l-adic properties of modular forms with quadratic nebentypus
and l-regular partition congruences
*Abstract:* In this talk, we discuss a framework for studying l-regular
partitions by defining a sequence of modular forms of level l and quadratic
character which encode the l-adic behavior of the so-called l-regular
partitions. We show that this sequence is congruent modulo increasing
powers of l to level 1 modular forms of increasing weights. We then prove
that certain modules generated by our sequence are isomorphic to certain
subspaces of level 1 cusp forms of weight independent of the power of l,
leading to a uniform bound on the ranks of those modules and consequently
to l-adic relations between l-regular partition values. This generalizes
earlier work of Folsom, Kent and Ono on the partition function, where the
relevant forms had no nebentypus, and is joint work with Mostafa Ghazy.


*Date and Time: *Thursday, October 24, 19:30 Allahabad, 17:30 Tahran, 17:00
Istanbul
*Zoom link:* https://kocun.zoom.us/j/99715471656
*Meeting ID: *997 1547 1656
*passcode:* 848084

*ICS-File: *https://researchseminars.org/seminar/FGC-IPM/ics

We hope to see you all,

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