Masaaki Furusawa's Books

Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].

Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.

Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of B{uml}ocherer's conjecture on the central critical values of the degree four L-functions for GSp(4), and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.

Statement of results Gauss sum, Kloosterman sum and Salie sum Matrix argument Kloosterman sums Evaluation of the Novodvorsky orbital integral Evaluation of the Bessel orbital integral Evaluation of the quadratic orbital integral Bibliography.

Book's by Masaaki Furusawa

On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma

On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma

On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III

On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III

On Central Critical Values of the Degree Four L-Functions for Gsp (4)

On Central Critical Values of the Degree Four L-Functions for Gsp (4)

On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma

On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma

On Central Critical Values of the Degree Four L-Functions for Gsp(4)

On Central Critical Values of the Degree Four L-Functions for Gsp(4)

Username

Password

Username

Password

Password again

Birthday

Email