Automorphic representations and analytic number theory on higher rank reductive
时间： 每周三、周四 9:50-11:25 2020-9-14 ~ 12-4
We shall first discuss some backgrounds on the global and local representation theories and tools for higher rank reductive groups, at least for GL(3). Topics will include, but no limited, to Whittaker/Kirillov model, pre-trace formula, Kuznetsov trace formula, compact induction/parabolic induction, newform theory, Rankin-Selberg theory, etc. Then we shall try to see if these tools can help us to generalize some recent works on sup norm problem and subconvexity bound for L-functions on GL(2) to more general groups.
Automorphic representations of GL(2). Some interest in analytic number theory.
1. I. N. Bernstein and A. V. Zelevinsky. Induced representations of reductive p-adic groups.
2. C.Bushnell and P.C.Kutzko. The admissible dual of GL(N) via compact open subgroups.3. N.Matringe. Essential Whittaker Functions for GL(n).