On Central Critical Values of the Degree Four $L$-functions for $/mathrm {GSp}(4)$ (eBook)

The Fundamental Lemma

Masaaki Furusawa (Autor)

eBook Download: PDF

139 Seiten
American Mathematical Society (Verlag)
978-1-4704-0380-5 (ISBN)

Infos

In this paper we prove two equalities of local Kloosterman integrals on $/mathrm{GSp}/left(4/right)$, the group of $4$ by $4$ symplectic similitude matrices. One is an equality between the Novodvorsky orbital integral and the Bessel orbital integral and the other one is an equality between the Bessel orbital integral and the quadratic orbital integral. We conjecture that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $/mathrm{gl}/left(2/right)$ in [{J1}] and [{J2}], where Jacquet has given another proof of Waldspurger's result [{W2}], generalize to the ones for the central critical values of the degree four spinor $L$-functions for $/mathrm{GSp}/left(4/right)$. We believe that our approach will lead us to a proof and also a precise formulation of a conjecture of Boecherer [{B}] and its generalization. Support for this conjecture may be found in the important paper of Boecherer and Schulze-Pillot [{BSP}]. Also a numerical evidence has been recently given by Kohnen and Kuss [{KK}]. Our results serve as the fundamental lemmas for our conjectural relative trace formulas for the main relevant double cosets.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 1-4704-0380-3 / 1470403803
• ISBN-13: 978-1-4704-0380-5 / 9781470403805