Speaker:Shigeru Kanemitsu (Kinki University,Japan） Venue: B1044 Time: 2017年09月21日 09:00-10:00 Title: On the Kuznetsov sum formula. Abstract:In the theory of automorphic L-functions, the Kuznetsov trace formula (Spectral part in terms of Kloostermann sums) is one of the highlights. In the famous books by Iwaniec and Motohashi, the formula has different outlook, mainly because Motohashi avoided the use of Sears-Titchmarsh expansion. In the talk we shall elucidate Motohashi's proof of the Kuznetsov sum formula (which is an expression of Kloosterman sum part in terms of spectral part, called the revesre Bruggeman-Kuznetsov formula in Iwaniec) in the light of Iwaniec argument by recoursing to special functions. Motohashi's method is a completion of Selberg's own idea, elaborated by Kuznetsov, of equating two expressions of the inner product of two real analytic Poincare series. One is from unfolding and the other from the Parseval. The Kuznetsov trace formula is, as described in Iwaniec as a Poisson summation formula, is a consequence of the functional equation of J. Fay.