In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands' beyond endoscopy proposal. These partition identities motivate an explicit plethysm expansion of SymjpSymkV q for GL2 in the case k " 3. We compute the plethysm explicitly for the cases k " 3, 4. Moreover, we use these expansions to explicitly compute the basic function attached to the symmetric power L-function of GL2 for these two cases.
MSC Codes Primary 11P84, 11S40, Secondary 05E05, 05E10
|Publication status||Published - 2017 Jun 9|
All Science Journal Classification (ASJC) codes