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)

Author: Masaaki Furusawa

Publisher:

Published: 2014-09-11

Total Pages: 134

ISBN-13: 9781470410575

DOWNLOAD EBOOK

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.

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

Author: Masaaki Furusawa

Publisher: American Mathematical Soc.

Published: 2013-08-23

Total Pages: 150

ISBN-13: 0821887424

DOWNLOAD 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.

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

Author: Masaaki Furusawa

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 158

ISBN-13: 0821833286

DOWNLOAD EBOOK

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}].

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)

Author: Masaaki Furusawa

Publisher:

Published: 2014-09-11

Total Pages: 139

ISBN-13: 9781470403805

DOWNLOAD EBOOK

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.

Recent Advances in Hodge Theory
Recent Advances in Hodge Theory

Author: Matt Kerr

Publisher: Cambridge University Press

Published: 2016-02-04

Total Pages: 533

ISBN-13: 1316531392

DOWNLOAD EBOOK

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.

Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness
Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness

Author: Lee Klingler

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 187

ISBN-13: 0821837389

DOWNLOAD EBOOK

This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)

On the Spectra of Quantum Groups
On the Spectra of Quantum Groups

Author: Milen Yakimov

Publisher: American Mathematical Soc.

Published: 2014-04-07

Total Pages: 104

ISBN-13: 082189174X

DOWNLOAD EBOOK

Joseph and Hodges-Levasseur (in the A case) described the spectra of all quantum function algebras on simple algebraic groups in terms of the centers of certain localizations of quotients of by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centers were only known up to finite extensions. The author determines the centers explicitly under the general conditions that the deformation parameter is not a root of unity and without any restriction on the characteristic of the ground field. From it he deduces a more explicit description of all prime ideals of than the previously known ones and an explicit parametrization of .

Operator-Valued Measures, Dilations, and the Theory of Frames
Operator-Valued Measures, Dilations, and the Theory of Frames

Author: Deguang Han

Publisher: American Mathematical Soc.

Published: 2014-04-07

Total Pages: 98

ISBN-13: 0821891723

DOWNLOAD EBOOK

The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between -algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or weakly, or w*) continuous.