On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III
Masaaki Furusawa · Kimball Martin · Joseph A. Shalika
Aug 2013 · American Mathematical Soc.
Ebook
134
Pages
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About this ebook
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.
formulas to prove generalizations of Böcherer's conjecture on the
central critical values of the degree four
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.
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