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SUMMARY:Naomi Sweeting (Princeton University)
DTSTART:20251125T210000Z
DTEND:20251125T220000Z
DTSTAMP:20260423T130605Z
UID:MITNT/125
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/125/">
 Arithmetic of Fourier coefficients of Gan-Gurevich lifts on $\\mathsf{G}_2
 $</a>\nby Naomi Sweeting (Princeton University) as part of MIT number theo
 ry seminar\n\nLecture held in Room 2-449 in the Simons Building (building 
 2).\n\nAbstract\nQuaternionic modular forms on $\\mathsf{G}_2$ carry a sur
 prisingly rich arithmetic structure. For example\, they have a theory of F
 ourier expansions where the Fourier coefficients are indexed by totally re
 al cubic rings. For quaternionic modular forms on $\\mathsf{G}_2$ associat
 ed via functoriality with certain modular forms on $\\mathrm{PGL}_2$\, Gro
 ss conjectured in 2000 that their Fourier coefficients encode $L$-values o
 f cubic twists of the modular form (echoing Waldspurger's work on Fourier 
 coefficients of half-integral weight modular forms). This talk will report
  on recent work proving Gross's conjecture when the modular forms are dihe
 dral\, giving the first examples for which it is known. Based on joint wor
 k with Petar Bakic\, Alex Horawa\, and Siyan Daniel Li-Huerta.\n
LOCATION:https://researchseminars.org/talk/MITNT/125/
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