Download or read book Eisenstein Series Via the Poincar Bundle and Applications written by Johannes Sprang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Eisenstein Series and Some Applications written by Helmut Klingen and published by . This book was released on 1984 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig and published by Cambridge Studies in Advanced. This book was released on 2018-07-05 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig and published by Cambridge University Press. This book was released on 2018-07-05 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.
Download or read book The 1 2 3 of Modular Forms written by Jan Hendrik Bruinier and published by Springer Science & Business Media. This book was released on 2008-02-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Download or read book Modular Forms a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Download or read book Some Applications of Modular Forms written by Peter Sarnak and published by Cambridge University Press. This book was released on 1990-11-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: 'expander graphs' and 'Ramanujan graphs'; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics and computer science.
Download or read book Spectral Methods of Automorphic Forms written by Henryk Iwaniec and published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain. This book was released on 2021-11-17 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.
Download or read book Borcherds Products on O 2 l and Chern Classes of Heegner Divisors written by Jan H. Bruinier and published by Springer. This book was released on 2004-10-11 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
Download or read book Automorphic Forms and L Functions for the Group GL n R written by Dorian Goldfeld and published by Cambridge University Press. This book was released on 2006-08-03 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
Download or read book Lectures on Geometry written by Nicholas Michael John Woodhouse and published by Oxford University Press. This book was released on 2017 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a series of chapters by leading researchers and practitioners on community engagement approaches in the field of counterterrorism and counterinsurgency. It presents existing and emerging community engagement models in various parts of the world which could serve as effective models for governments keen to work with community leaders to manage and reduce the terrorist threat. The book emphasizes the strength of communities as central to government approaches in countering violent extremism.
Download or read book Rational Points on Modular Elliptic Curves written by Henri Darmon and published by American Mathematical Soc.. This book was released on 2004 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Poincare Conjecture written by Donal O'Shea and published by Bloomsbury Publishing USA. This book was released on 2009-05-26 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.
Download or read book Berkeley Lectures on P adic Geometry written by Peter Scholze and published by Princeton University Press. This book was released on 2020-05-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
Download or read book Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change written by Jayce Getz and published by Springer Science & Business Media. This book was released on 2012-03-28 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1983 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
