Periods of T-motives and Special Functions in Characteristic P
Author: Samarendra Kumar Sinha
Publisher:
Published: 1995
Total Pages: 332
ISBN-13:
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Number Theory
Author: Michel Waldschmidt
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 410
ISBN-13: 0821806068
DOWNLOAD EBOOKTo observe the tenth anniversary of the founding of the Ramanujan Mathematical Society, an international conference on Discrete Mathematics and Number Theory was held in January 1996 in Tiruchirapalli, India. This volume contains proceedings from the number theory component of that conference. Papers are divided into four groups: arithmetic algebraic geometry, automorphic forms, elementary and analytic number theory, and transcendental number theory. This work deals with recent progress in current aspects of number theory and covers a wide variety of topics.
Arithmetic Geometry over Global Function Fields
Author: Gebhard Böckle
Publisher: Springer
Published: 2014-11-13
Total Pages: 350
ISBN-13: 3034808534
DOWNLOAD EBOOKThis volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.
Transcendence and Linear Relations of 1-Periods
Author: Annette Huber
Publisher: Cambridge University Press
Published: 2022-05-26
Total Pages: 266
ISBN-13: 1009022717
DOWNLOAD EBOOKThis exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of π, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.
Motives
Author: Uwe Jannsen
Publisher: American Mathematical Soc.
Published: 1994-02-28
Total Pages: 696
ISBN-13: 9780821827994
DOWNLOAD EBOOKMotives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field. Over the last ten years or so, researchers in various areas--Hodge theory, algebraic $K$-theory, polylogarithms, automorphic forms, $L$-functions, $ell$-adic representations, trigonometric sums, and algebraic cycles--have discovered that an enlarged (and in part conjectural) theory of ``mixed'' motives indicates and explains phenomena appearing in each area. Thus the theory holds the potential of enriching and unifying these areas. These two volumes contain the revised texts of nearly all the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.
Journal für die reine und angewandte Mathematik
Author: August Leopold Crelle
Publisher:
Published: 2002
Total Pages: 750
ISBN-13:
DOWNLOAD EBOOKFeatured Reviews in Mathematical Reviews 1997-1999
Author: Donald G. Babbitt
Publisher: American Mathematical Soc.
Published: 2000-05-05
Total Pages: 762
ISBN-13: 9780821896709
DOWNLOAD EBOOKThis second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
The Arithmetic of Function Fields
Author: David Goss
Publisher: Walter de Gruyter
Published: 2011-06-24
Total Pages: 493
ISBN-13: 3110886154
DOWNLOAD EBOOKThisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Dissertation Abstracts International
Author:
Publisher:
Published: 2007
Total Pages: 924
ISBN-13:
DOWNLOAD EBOOKTranscendence and Linear Relations of 1-Periods
Author: Annette Huber
Publisher: Cambridge University Press
Published: 2022-05-26
Total Pages: 265
ISBN-13: 1316519937
DOWNLOAD EBOOKLeading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.
