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Author: Peter Gustav Lejeune Dirichlet
Publisher: Cambridge University Press
Published: 2013-08-22
Total Pages: 651
ISBN-13: 1108050395
DOWNLOAD EBOOKThe third edition (1879) of Dirichlet's posthumously published 1856-7 lectures on number theory includes several famous proofs.
Author: B. Schoeneberg
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 244
ISBN-13: 3642656633
DOWNLOAD EBOOKThis book is a fully detailed introduction to the theory of modular functions of a single variable. I hope that it will fill gaps which in view ofthe lively development ofthis theory have often been an obstacle to the students' progress. The study of the book requires an elementary knowledge of algebra, number theory and topology and a deeper knowledge of the theory of functions. An extensive discussion of the modular group SL(2, Z) is followed by the introduction to the theory of automorphic functions and auto morphic forms of integral dimensions belonging to SL(2,Z). The theory is developed first via the Riemann mapping theorem and then again with the help of Eisenstein series. An investigation of the subgroups of SL(2, Z) and the introduction of automorphic functions and forms belonging to these groups folIows. Special attention is given to the subgroups of finite index in SL (2, Z) and, among these, to the so-called congruence groups. The decisive role in this setting is assumed by the Riemann-Roch theorem. Since its proof may be found in the literature, only the pertinent basic concepts are outlined. For the extension of the theory, special fields of modular functions in particular the transformation fields of order n-are studied. Eisen stein series of higher level are introduced which, in case of the dimension - 2, allow the construction of integrals of the 3 rd kind. The properties of these integrals are discussed at length.
Author: Calcutta Mathematical Society
Publisher:
Published: 1909
Total Pages: 392
ISBN-13:
DOWNLOAD EBOOKAuthor: GorÅ Shimura
Publisher: Princeton University Press
Published: 1971-08-21
Total Pages: 292
ISBN-13: 9780691080925
DOWNLOAD EBOOKThe theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Author: Srinivasa Ramanujan Aiyangar
Publisher: American Mathematical Soc.
Published: 1995-09-07
Total Pages: 366
ISBN-13: 9780821891254
DOWNLOAD EBOOKThe letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources. Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical result in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life. Ramanujan: Letters and Commentary was selected for the CHOICE list of Outstanding Academic Books for 1996.
Author: John S. Rose
Publisher: Courier Corporation
Published: 2013-05-27
Total Pages: 322
ISBN-13: 0486170667
DOWNLOAD EBOOKText for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.
Author: M. Hazewinkel
Publisher: Elsevier
Published: 2006-05-30
Total Pages: 543
ISBN-13: 0080462499
DOWNLOAD EBOOKAlgebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.- Thorough and practical source for information- Provides in-depth coverage of new topics in algebra- Includes references to relevant articles, books and lecture notes
Author: Einar Hille
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 510
ISBN-13: 9780821829141
DOWNLOAD EBOOKEmphasizes the conceptual and historical continuity of analytic function theory. This work covers topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It features chapters on majorization and on functions holomorphic in a half-plane.
Author: Ranjan Roy
Publisher: Cambridge University Press
Published: 2017-04-18
Total Pages: 491
ISBN-13: 1107159385
DOWNLOAD EBOOKA thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.
Author: N.L. Alling
Publisher: Elsevier
Published: 2011-08-18
Total Pages: 363
ISBN-13: 0080871658
DOWNLOAD EBOOKReal Elliptic Curves
