In this talk, we present our recent result on Deligne's conjecture for symmetric sixth \(L\)-functions of modular forms. We define automorphic periods associated to globally generic cuspidal automorphic representations of GSp\(_4\) and show that the algebraicity of critical \(L\)-values for GSp\(_4 \times\)GL\(_2\) can be expressed in terms of these periods. In the case of Kim–Ramakrishnan–Shahidi lifts of GL\(_2\), we establish period relations for the automorphic periods and powers of Petersson norm of modular forms.The conjecture for symmetric sixth \(L\)-functions then follows from our previous work on the algebraicity of adjoint \(L\)-functions for GSp\(_4\).
On Deligne's conjecture for symmetric sixth \(L\)-functions of modular forms
08.06.2021 14:30 - 16:00
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location:
Meeting ID: 431 655 310, Passcode: 0cnL5d