On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III PDF Download
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Author: Masaaki Furusawa
Publisher: American Mathematical Soc.
ISBN: 0821887424
Category : Mathematics
Languages : en
Pages : 150
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Book Description
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.
Author: Masaaki Furusawa
Publisher: American Mathematical Soc.
ISBN: 0821887424
Category : Mathematics
Languages : en
Pages : 150
Get Book
Book Description
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.
Author: Masaaki Furusawa
Publisher: American Mathematical Soc.
ISBN: 0821833286
Category : Mathematics
Languages : en
Pages : 158
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Book Description
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}].
Author: Masaaki Furusawa
Publisher:
ISBN: 9781470410575
Category : Automorphic forms
Languages : en
Pages : 134
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Book Description
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.
Author: Ameya Pitale
Publisher: American Mathematical Soc.
ISBN: 0821898566
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and
Author: Matt Kerr
Publisher: Cambridge University Press
ISBN: 1316531392
Category : Mathematics
Languages : en
Pages : 533
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Book Description
In its simplest form, Hodge theory is the study of periods – integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.
Author: Yuri Tschinkel
Publisher: Universitätsverlag Göttingen
ISBN: 3938616776
Category : Algebraic varieties
Languages : en
Pages : 168
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Book Description
Author: Nicole Bopp
Publisher: American Mathematical Soc.
ISBN: 0821836234
Category : Mathematics
Languages : en
Pages : 250
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Book Description
Intends to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces.
Author:
Publisher: American Mathematical Soc.
ISBN: 0821834959
Category :
Languages : en
Pages : 154
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Book Description
Author:
Publisher: American Mathematical Soc.
ISBN: 0821834452
Category :
Languages : en
Pages : 102
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Book Description
Author: Jason Fulman
Publisher: American Mathematical Soc.
ISBN: 0821837060
Category : Mathematics
Languages : en
Pages : 104
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Book Description
Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.
