[Turkmath:7351] Aralık 17, 2025 saat 17:00:: FGC-HRI-IPM Sayılar Teorisi Semineri::Lejla Smajlovic

[kazimilhan.ikeda]

Değerli Matematikçiler,

Aşağıda 17 Aralık Çarşamba günü saat 17:00'da yapılacak FGC-HRI-IPM 
Sayılar Teorisi Seminerinin detaylarını bulacaksınız.

Saygılarımla,
İlhan İkeda

-------------

Dear all,

Our next speaker is Lejla Smajlovic from the University of Sarajevo.

Date: Wednesday, December 17

Time: 17:00 (Istanbul LT), 17:30 (Tehran LT), 19:30 (Allahabad LT)

Speaker: Lejla Smajlovic
Title: On some nonholomorphic automorphic forms, their inner products 
and generating functions

Abstract:
In this talk we focus on the following three automorphic forms on a 
Fuchsian group of the first kind with at least one cusp: the Eisenstein 
series, the Niebur–Poincaré series associated to the cusp at infinity, 
and the resolvent kernel/Green's function. We discuss how these 
functions can be viewed as building blocks for describing log-norms of 
certain meromorphic functions in terms of their divisors and derive a 
generalization of a Rorlich–Jensen type formula, based on an evaluation 
of the Petersson inner product of the Niebur–Poincaré series with a 
suitably regularized Green's function.

We then turn our attention to the generating functions of the 
Niebur–Poincaré series and its derivative at s=1. Both functions depend 
on two variables in the upper half-plane. We prove that, for any 
Fuchsian group of the first kind, the generating function of the 
Niebur–Poincaré series in each variable is a polar harmonic Maass form 
of a certain weight, describe its polar part, and explain how it serves 
as a building block for describing weight two meromorphic modular forms 
in terms of their divisors.

Moreover, we show that the generating function of the derivative of the 
Niebur–Poincaré series at s=1 can be expressed—up to a certain function 
appearing in the Kronecker limit formula—as a derivative of an 
automorphic kernel associated with a new point-pair invariant expressed 
in terms of the Rogers dilogarithm.

This talk is based on joint work with Kathrin Bringmann, James Cogdell, 
and Jay Jorgenson.

Zoom details:
Zoom link: https://kocun.zoom.us/j/99715471656
Meeting ID: 997 1547 1656
Passcode: 848084

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