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SUMMARY:Aaron Pollack (UCSD)
DTSTART:20220217T220000Z
DTEND:20220217T230000Z
DTSTAMP:20260423T005847Z
UID:UCSD_NTS/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/56/
 ">A Cohen-Zagier modular form on G_2</a>\nby Aaron Pollack (UCSD) as part 
 of UCSD number theory seminar\n\nLecture held in APM 6402 and online.\n\nA
 bstract\nI will report on joint work with Spencer Leslie where we define a
 n analogue of the Cohen-Zagier Eisenstein series to the exceptional group 
 $G_2$. Recall that the Cohen-Zagier Eisenstein series is a weight $3/2$ mo
 dular form whose Fourier coefficients see the class numbers of imaginary q
 uadratic fields. We define a particular modular form of weight $1/2$ on $G
 _2$\, and prove that its Fourier coefficients see (certain torsors for) th
 e 2-torsion in the narrow class groups of totally real cubic fields. In pa
 rticular: 1) we define a notion of modular forms of half-integral weight o
 n certain exceptional groups\, 2) we prove that these modular forms have a
  nice theory of Fourier coefficients\, and 3) we partially compute the Fou
 rier coefficients of a particular nice example on G_2.\n\npre-talk at 1:20
 pm\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/56/
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