A LOCAL RELATIVE TRACE FORMULA FOR PGL(2)

作者：Delorme Patrick^*; Harinck Pascale

来源：Pacific Journal of Mathematics, 2017, 291(1): 121-147.

DOI：10.2140/pjm.2017.291.121

• p-adic reductive groups
• symmetric spaces
• local relative trace formula
• truncated kernel
• regularized periods

Following a scheme inspired by recent results of B. Feigon, who obtained what she called a local relative trace formula for PGL(2) and a local Kuznetsov trace formula for U(2), we describe the spectral side of a local relative trace formula for G := PGL (2,E) relative to the symmetric subgroup H : D PGL(2,F) where E/F is an unramified quadratic extension of local nonarchimedean fields of characteristic 0. The spectral side is given in terms of regularized normalized periods and normalized C-functions of HarishChandra. Using the geometric side of the local relative trace formula obtained in a more general setting by the authors and S. Souaifi, we deduce a local relative trace formula for G relative to H. We apply our result to invert some orbital integrals.

• 出版日期2017-11