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SUMMARY:Aaron Pollack (UC San Diego)
DTSTART:20231005T210000Z
DTEND:20231005T220000Z
DTSTAMP:20260423T022806Z
UID:UCSD_NTS/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/99/
 ">Arithmeticity of quaternionic modular forms on G_2</a>\nby Aaron Pollack
  (UC San Diego) as part of UCSD number theory seminar\n\nLecture held in A
 PM 6402 and online.\n\nAbstract\nQuaternionic modular forms (QMFs) on the 
 split exceptional group G_2 are a special class of automorphic functions o
 n this group\, whose origin goes back to work of Gross-Wallach and Gan-Gro
 ss-Savin.  While the group G_2 does not possess any holomorphic modular fo
 rms\, the quaternionic modular forms seem to be able to be a good substitu
 te.  In particular\, QMFs on G_2 possess a semi-classical Fourier expansio
 n and Fourier coefficients\, just like holomorphic modular forms on Shimur
 a varieties.  I will explain the proof that the cuspidal QMFs of even weig
 ht at least 6 admit an arithmetic structure: there is a basis of the space
  of all such cusp forms\, for which every Fourier coefficient of every ele
 ment of this basis lies in the cyclotomic extension of Q.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/99/
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