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Author : Glenn Howard Stevens
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (769 download)
Download or read book On Congruences Satisfied by Special Values of L-functions written by Glenn Howard Stevens and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Urbanowicz
Publisher : Springer Science & Business Media
ISBN 13 : 9780792363798
Total Pages : 284 pages
Book Rating : 4.3/5 (637 download)
Download or read book Congruences for L-Functions written by J. Urbanowicz and published by Springer Science & Business Media. This book was released on 2000-06-30 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and up-to-date treatment of research carried out in the last twenty years on congruences involving the values of L-functions (attached to quadratic characters) at certain special values. There is no other book on the market which deals with this subject. The book presents in a unified way congruences found by many authors over the years, from the classical ones of Gauss and Dirichlet to the recent ones of Gras, Vehara, and others. Audience: This book is aimed at graduate students and researchers interested in (analytic) number theory, functions of a complex variable and special functions.
Author : M. Rapoport
Publisher :
ISBN 13 :
Total Pages : 408 pages
Book Rating : 4.3/5 (91 download)
Download or read book Beilinson's Conjectures on Special Values of L-functions written by M. Rapoport and published by . This book was released on 1988 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James W. Cogdell
Publisher : Walter de Gruyter
ISBN 13 : 3110892707
Total Pages : 441 pages
Book Rating : 4.1/5 (18 download)
Download or read book Automorphic Representations, L-Functions and Applications: Progress and Prospects written by James W. Cogdell and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.
Author : Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 1489966994
Total Pages : 366 pages
Book Rating : 4.4/5 (899 download)
Download or read book Number Theory Related to Fermat’s Last Theorem written by Koblitz and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michel Courtieu
Publisher : Springer
ISBN 13 : 3540451781
Total Pages : 202 pages
Book Rating : 4.5/5 (44 download)
Download or read book Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms written by Michel Courtieu and published by Springer. This book was released on 2003-12-09 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book will be very useful for postgraduate students and for non-experts looking for a quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.
Author : G. Stevens
Publisher : Springer Science & Business Media
ISBN 13 : 1468491652
Total Pages : 233 pages
Book Rating : 4.4/5 (684 download)
Download or read book Arithmetic on Modular Curves written by G. Stevens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most intriguing problems of modern number theory is to relate the arithmetic of abelian varieties to the special values of associated L-functions. A very precise conjecture has been formulated for elliptic curves by Birc~ and Swinnerton-Dyer and generalized to abelian varieties by Tate. The numerical evidence is quite encouraging. A weakened form of the conjectures has been verified for CM elliptic curves by Coates and Wiles, and recently strengthened by K. Rubin. But a general proof of the conjectures seems still to be a long way off. A few years ago, B. Mazur [26] proved a weak analog of these c- jectures. Let N be prime, and be a weight two newform for r 0 (N) . For a primitive Dirichlet character X of conductor prime to N, let i\ f (X) denote the algebraic part of L (f , X, 1) (see below). Mazur showed in [ 26] that the residue class of Af (X) modulo the "Eisenstein" ideal gives information about the arithmetic of Xo (N). There are two aspects to his work: congruence formulae for the values Af(X) , and a descent argument. Mazur's congruence formulae were extended to r 1 (N), N prime, by S. Kamienny and the author [17], and in a paper which will appear shortly, Kamienny has generalized the descent argument to this case.
Author : J. Urbanowicz
Publisher : Springer Science & Business Media
ISBN 13 : 9401595429
Total Pages : 266 pages
Book Rating : 4.4/5 (15 download)
Download or read book Congruences for L-Functions written by J. Urbanowicz and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2. Their congruence provided a unified setting for many congruences proved previously by other authors using various means. The Hardy-Williams idea was as follows. Let d be the discriminant of a quadratic field. Suppose that d is odd and let d = PIP2· . . Pn be its unique decomposition into prime discriminants. Then, for any positive integer k coprime with d, the congruence holds trivially as each Legendre-Jacobi-Kronecker symbol (~) has the value + 1 or -1. Expanding this product gives ~ eld e:=l (mod4) where e runs through the positive and negative divisors of d and v (e) denotes the number of distinct prime factors of e. Summing this congruence for o
Author : Bruce C. Berndt
Publisher : Springer Science & Business Media
ISBN 13 : 1461240867
Total Pages : 453 pages
Book Rating : 4.4/5 (612 download)
Download or read book Analytic Number Theory written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: On May 16 -20, 1995, approximately 150 mathematicians gathered at the Conference Center of the University of Illinois at Allerton Park for an Inter national Conference on Analytic Number Theory. The meeting marked the approaching official retirement of Heini Halberstam from the mathematics fac ulty of the University of Illinois at Urbana-Champaign. Professor Halberstam has been at the University since 1980, for 8 years as head of the Department of Mathematics, and has been a leading researcher and teacher in number theory for over forty years. The program included invited one hour lectures by G. Andrews, J. Bour gain, J. M. Deshouillers, H. Halberstam, D. R. Heath-Brown, H. Iwaniec, H. L. Montgomery, R. Murty, C. Pomerance, and R. C. Vaughan, and almost one hundred other talks of varying lengths. These volumes comprise contributions from most of the principal speakers and from many of the other participants, as well as some papers from mathematicians who were unable to attend. The contents span a broad range of themes from contemporary number theory, with the majority having an analytic flavor.
Author : M. Ram Murty
Publisher : Springer Science & Business Media
ISBN 13 : 3034802749
Total Pages : 206 pages
Book Rating : 4.0/5 (348 download)
Download or read book Non-vanishing of L-Functions and Applications written by M. Ram Murty and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. It begins at a very basic level and continues to develop, providing readers with a theoretical foundation that allows them to understand the latest discoveries in the field.
Author : Brett A. Tangedal
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (318 download)
Download or read book The Conjectures of Sands and Stark for Special Values of Abelian L-functions written by Brett A. Tangedal and published by . This book was released on 1994 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jürgen Neukirch
Publisher : Springer Science & Business Media
ISBN 13 : 9783540378884
Total Pages : 856 pages
Book Rating : 4.3/5 (788 download)
Download or read book Cohomology of Number Fields written by Jürgen Neukirch and published by Springer Science & Business Media. This book was released on 2008-02-18 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.
Author : Jr̲n Steuding
Publisher : Springer Science & Business Media
ISBN 13 : 3540265260
Total Pages : 320 pages
Book Rating : 4.5/5 (42 download)
Download or read book Value-Distribution of L-Functions written by Jr̲n Steuding and published by Springer Science & Business Media. This book was released on 2007-06-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
Author : James Carlson
Publisher : American Mathematical Society, Clay Mathematics Institute
ISBN 13 : 1470474603
Total Pages : 185 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Millennium Prize Problems written by James Carlson and published by American Mathematical Society, Clay Mathematics Institute. This book was released on 2023-09-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: On August 8, 1900, at the second International Congress of Mathematicians in Paris, David Hilbert delivered his famous lecture in which he described twenty-three problems that were to play an influential role in mathematical research. A century later, on May 24, 2000, at a meeting at the Collège de France, the Clay Mathematics Institute (CMI) announced the creation of a US$7 million prize fund for the solution of seven important classic problems which have resisted solution. The prize fund is divided equally among the seven problems. There is no time limit for their solution. The Millennium Prize Problems were selected by the founding Scientific Advisory Board of CMI—Alain Connes, Arthur Jaffe, Andrew Wiles, and Edward Witten—after consulting with other leading mathematicians. Their aim was somewhat different than that of Hilbert: not to define new challenges, but to record some of the most difficult issues with which mathematicians were struggling at the turn of the second millennium; to recognize achievement in mathematics of historical dimension; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; and to emphasize the importance of working towards a solution of the deepest, most difficult problems. The present volume sets forth the official description of each of the seven problems and the rules governing the prizes. It also contains an essay by Jeremy Gray on the history of prize problems in mathematics.
Author : Alexei A. Panchishkin
Publisher : Springer
ISBN 13 : 3662215411
Total Pages : 167 pages
Book Rating : 4.6/5 (622 download)
Download or read book Non-Archimedean L-Functions written by Alexei A. Panchishkin and published by Springer. This book was released on 2013-11-11 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:. 1, and we may regard C as the group of all continuous quasicharacters C = Hom(R~, c>
Author : Günter Harder
Publisher : Princeton University Press
ISBN 13 : 0691197881
Total Pages : 234 pages
Book Rating : 4.6/5 (911 download)
Download or read book Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions written by Günter Harder and published by Princeton University Press. This book was released on 2019-12-03 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- The cohomology of GLn -- Analytic tools -- Boundary cohomology -- The strongly inner spectrum and applications -- Eisenstein cohomology -- L-functions -- Harish-Chandra modules over Z / by Günter Harder -- Archimedean intertwining operator / by Uwe Weselmann.
Author : David Ginzburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821847082
Total Pages : 339 pages
Book Rating : 4.8/5 (218 download)
Download or read book Automorphic Forms and $L$-functions II written by David Ginzburg and published by American Mathematical Soc.. This book was released on 2009 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.
