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SUMMARY:Ye Tian (Morningside Center of Math.\, Beijing)
DTSTART:20220407T213000Z
DTEND:20220407T223000Z
DTSTAMP:20260423T022841Z
UID:JNTS/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/42/">On
  Tunnell-Gross type formulae</a>\nby Ye Tian (Morningside Center of Math.\
 , Beijing) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstrac
 t\nFor a weight 2 cuspidal newform $f\,$  we prove an explicit version of 
 Waldspurger's theorem\, which relates  L-values of quadratic twists of $f$
   to certain ternary quadratic forms.  Gross gave a geometric proof of suc
 h a formula assuming (i) the conductor of $f $ is a prime (ii) L(1\, $f$) 
 is nonzero. Gross' work was generalized by Bocherer and Schulze-Pillot to 
 square-free conductors based on their investigation of Yoshida lift. Via a
  different approach\,  Mao generalized Gross' work only assuming (i).  In 
 this talk\, we outline the proof of an explicit formula in the general cas
 e.  Joint work with W. He and W. Xiong.\n
LOCATION:https://researchseminars.org/talk/JNTS/42/
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