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SUMMARY:The arithmetic of Fourier coefficients of automorphic forms on G2 
 [Arithmetic Geometry and Representation Theory Research Seminar]
DTSTART:20251128T130500Z
DTEND:20251128T150000Z
DTSTAMP:20260314T232000Z
UID:indico-event-782@math-events.uni-bonn.de
DESCRIPTION:Speakers: Aleksander Horawa (University of Bonn)\n\nShimura (1
 973) discovered a way to associate a holomorphic half-integral weight modu
 lar form h with a classical cusp form f. Subsequently\, Waldspurger (1980
 s) proved a remarkable formula relating squares of the Fourier coefficient
 s of h and quadratic twists of L-values of f. We prove that one can assoc
 iate "quaternionic" modular forms on the algebraic group G2 with dihedral 
 cusp forms f whose Fourier coefficients are explicitly related to cubic tw
 ists of L-values of f. This gives the first examples where a conjecture of
  Gross (2000) has been fully verified. (Joint work with Petar Bakić\, Siy
 an Daniel Li-Huerta\, and Naomi Sweeting.)\n\nhttps://math-events.uni-bonn
 .de/event/782/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/782/
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