BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UC San Diego)
DTSTART:20211122T230000Z
DTEND:20211122T235000Z
DTSTAMP:20260423T041510Z
UID:UCLA_NTS/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/40/
 ">A Cohen-Zagier modular form on G_2</a>\nby Aaron Pollack (UC San Diego) 
 as part of UCLA Number Theory Seminar\n\nLecture held in Math Science Buil
 ding 5203.\n\nAbstract\nI will report on joint work-in-progress with Spenc
 er Leslie where we define an analogue of the Cohen-Zagier Eisenstein serie
 s to the exceptional group G_2. Recall that the Cohen-Zagier Eisenstein se
 ries is a weight 3/2 modular form whose Fourier coefficients see the class
  numbers of imaginary quadratic fields. We define a particular modular for
 m of weight 1/2 on G_2\, and prove that its Fourier coefficients see the 2
 -torsion in the narrow class groups of totally real cubic fields. In parti
 cular: 1) we define a notion of modular forms of half-integral weight on c
 ertain exceptional groups\, 2) we prove that these modular forms have a ni
 ce theory of Fourier coefficients\, and 3) we partially compute the Fourie
 r coefficients of a particular nice example on G_2.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/40/
END:VEVENT
END:VCALENDAR