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# π On central critical values of the degree four L-functions for GSp(4): the fundamental lemma. III by Masaaki Furusawa, Kimball Martin, Joseph A. Shalika β free epub

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Some time ago, the first and third authors proposed two relative trace formulas to prove generalisations of Bocherer's conjecture on the central critical values of the degree four $L$-functions for $\mathrm{GSp}(4)$, 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

## About book:

## About file:

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- Series:
**Memoirs of the American Mathematical Society 1057** - Author:
**Masaaki Furusawa, Kimball Martin, Joseph A. Shalika** - Year:
**2013** - Publisher:
**Amer Mathematical Society** - Language:
**English** - ISBN:
**0821887424,978-0-8218-8742-4,0-8218-3328-6**

- File size:
**954 091** - Format:
**pdf**

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This is a text on the mean-value and omega theorems for the Riemann Zeta-function. It includes discussion of some fundamental theorems on Titchmarsh series and applications, and Titchmarsh's Phenomenon....

Beilinsons Conjectures on Special Values of L-Functions deals with Alexander Beilinsons conjectures on special values of L-functions. Topics covered range from Pierre Delignes conjecture on critical values of L-functions to the Deligne-Beilinson cohomolog...

The Central Nervous System: Structure and Function, Fourth Edition continues the tradition of one of the most respected textbooks in clinical neuroscience by providing medical students the knowledge and understanding of neuroscience as a basis for clinica...

IX The International Seminar on the Immunological System as a Target for Toxic Damage was held at The Commission of the European Communities (CEC) in Luxembourg on 6-9 November 1984. It was organized by the CEC and the International Programme on Chemical ...

Fragility functions constitute an emerging tool for the probabilistic seismic risk assessment of buildings, infrastructures and lifeline systems. The work presented in this book is a partial product of a European Union funded research project SYNER-G (FP7...

As Morgan Stanley's chief Asia specialist, getting Asia right is Stephen Roach's personal obsession, and this in-depth compilation represents more than 70 of Roach's key research efforts not just on Asia, but also on how the region fits into the broad con...

Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is u...

Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is u...

The U.S. Environmental Protection Agencyβs New Source Review (NSR) programs are designed to help ensure that the construction or modification of factories, electric-generating facilities and other large stationary sources of pollutants will meet emissions...