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SUMMARY:Modular forms of half-integral weight on G_2 - Aaron Pollack (Univ
 ersity of California\, San Diego)
DTSTART:20220825T090000Z
DTEND:20220825T100000Z
UID:TALK177239@talks.cam.ac.uk
DESCRIPTION:Classical holomorphic modular forms are number-theoretic objec
 ts that have been intensely studied. The split exceptional group G_2 does 
 not support a theory of holomorphic modular forms\, but it does possess so
 -called quaternionic modular forms. These are a special class of automorph
 ic forms that appear to behave similarly to holomorphic modular forms. In 
 the talk\, I will describe a theory of modular forms of half-integral weig
 ht on G_2 and other exceptional groups. In particular\, we prove the exist
 ence of a modular form of weight 1/2 on G_2 whose Fourier coefficients are
  related to the 2-torsion in the narrow class groups of totally real cubic
  fields.\nThis is joint work with Spencer Leslie (Boston College).
LOCATION:Seminar Room 1\, Newton Institute
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