BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lejla Smajlovic DTSTART:20251217T140000Z DTEND:20251217T150000Z DTSTAMP:20260422T104731Z UID:FGC-IPM/62 DESCRIPTION:Title: On some nonholomorphic automorphic forms\, their inner products and gener ating functions\nby Lejla Smajlovic as part of FGC-HRI-IPM Number Theo ry Webinars\n\n\nAbstract\nIn this talk we focus on the following three au tomorphic forms on a Fuchsian group of the first kind with at least one cu sp: the Eisenstein series and the Niebur-Poincaré series associated to th e cusp at infinity\, and the resolvent kernel/Green's function. We discuss how those functions can be viewed as building blocks for describing log-n orms of some meromorphic functions in terms of their divisors and derive a generalization of the Rorlich-Jensen type formula\, which is based on an evaluation of the Petersson inner product of the Niebur-Poincaré series w ith the suitably regularized Green's function. Then\, we turn our attentio n to the generating functions of the Niebur-Poincaré series and its deriv ative at s=1. Both functions depend upon two variables in the upper half-p lane. We prove that\, for any Fuchsian group of the first kind\, the gener ating function of the Niebur-Poincaré series in each variable is a polar harmonic Maass form of a certain weight\, describe its polar part and disc uss how it can be viewed as a building block for describing weight two mer omorphic modular forms in terms of their divisors. Moreover\, we prove tha t 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 Krone cker limit formula\, as a derivative of an automorphic kernel associated t o a new point-pair invariant expressed in terms of the Rogers dilogarithm. \n\nThe talk is based on the joint work with Kathrin Bringmann\, James Cog dell and Jay Jorgenson.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/62/ END:VEVENT END:VCALENDAR