Eisenstein Series, Trace Formulas and Applications(II)

Time/Location: 5-6 TUE, C701

Syllabus:

Eisenstein Series, Trace Formulas and Applications (I)

1. Kuznetsov Trace Formula and Applications [1,2]

     1. Kloosterman sums

     2. Poincare series

     3. Kuznetsov trace formula

     4. Sums of Kloosterman sum

2. Trace Formula and Applications [3,4,5]

   Main reference: Gelbart and Jacquet, Forms of GL(2) from the analytic point of view.

         1, Trace formula for compact quotients 

         2. Cusp forms on GL(2)

         3. P-series

         4. Analytic continuation of M(s)

         5, Eisenstein series

         6, The trace formula

         7, A second form of the trace formula

         8, Applications to quaternion algebras

References：

1. Ye, Modular forms and trace fromula.

2. Iwaniec, Spectral methods of automorphic forms.

3. Bump, Automorohic forms and Representations.

4. Gelbart and Jacquet, Forms of GL(2) from the analytic point of view.

5. Gelbert, Lectures on Arthur-Selberg trace formula.