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>
Download or read book Non Archimedean L functions of Siegel and Hilbert Modular Forms written by Alekseĭ Alekseevich Panchishkin and published by Springer. This book was released on 1991 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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 2003-12-05 with total page 204 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.
Download or read book Non Archimedean L Functions and Arithmetical Siegel Modular Forms written by Michel Courtieu and published by . This book was released on 2014-09-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iwasawa Theory 2012 written by Thanasis Bouganis and published by Springer. This book was released on 2014-12-08 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).
Download or read book Elliptic Curves Modular Forms and Iwasawa Theory written by David Loeffler and published by Springer. This book was released on 2017-01-15 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.
Download or read book Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms written by Kazuyuki Hatada and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Automorphic Forms and Related Geometry Assessing the Legacy of I I Piatetski Shapiro written by James W. Cogdell and published by American Mathematical Soc.. This book was released on 2014-04-01 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
Download or read book Iwasawa Theory and Its Perspective Volume 2 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2024-04-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
Download or read book Elementary Theory of L functions and Eisenstein Series written by Haruzo Hida and published by Cambridge University Press. This book was released on 1993-02-11 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.
Download or read book Sammlung written by and published by World Scientific. This book was released on 1996 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk ?Mathematics as Metaphor? summarises the author's view on mathematics as an outgrowth of natural language.
Download or read book Selected Papers Of Yu I Manin written by Yu I Manin and published by World Scientific. This book was released on 1996-06-28 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk “Mathematics as Metaphor” summarises the author's view on mathematics as an outgrowth of natural language.
Download or read book Arithmetic and Geometry written by Luis Dieulefait and published by Cambridge University Press. This book was released on 2015-10-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.
Download or read book Real Functions Current Topics written by Vasile Ene and published by Springer. This book was released on 2006-11-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books devoted to the theory of the integral have ignored the nonabsolute integrals, despite the fact that the journal literature relating to these has become richer and richer. The aim of this monograph is to fill this gap, to perform a study on the large number of classes of real functions which have been introduced in this context, and to illustrate them with many examples. This book reports on some recent advances in the theory of real functions and can serve as a textbook for a course in the subject, and to stimulate further research in this exciting field.
Download or read book Motives written by and published by American Mathematical Soc.. This book was released on 1994-02-28 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.
Download or read book Introduction to Cyclotomic Fields written by Lawrence C. Washington and published by Springer Science & Business Media. This book was released on 1997 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.
