Lectures on Modular Forms

Lectures on Modular Forms
Author: Robert C. Gunning
Publisher: Princeton University Press
Total Pages: 116
Release: 1962-03-21
Genre: Education
ISBN: 9780691079950

New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H. C. Gunning's book surveys techniques and problems; only the simpler cases are treated-modular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone.

Lectures on Modular Forms

Lectures on Modular Forms
Author: Joseph J. Lehner
Publisher: Courier Dover Publications
Total Pages: 99
Release: 2017-05-17
Genre: Mathematics
ISBN: 0486821404

Concise book offers expository account of theory of modular forms and its application to number theory and analysis. Substantial notes at the end of each chapter amplify the more difficult subjects. 1969 edition.

Computations with Modular Forms

Computations with Modular Forms
Author: Gebhard Böckle
Publisher: Springer Science & Business Media
Total Pages: 377
Release: 2014-01-23
Genre: Mathematics
ISBN: 3319038478

This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.

An Introduction to Finite Tight Frames

An Introduction to Finite Tight Frames
Author: Shayne F. D. Waldron
Publisher: Springer
Total Pages: 590
Release: 2018-02-03
Genre: Mathematics
ISBN: 0817648151

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook for a graduate course or seminar involving finite frames. The self-contained, user-friendly presentation also makes the work useful as a self-study resource or reference for graduate students, instructors, researchers, and practitioners in pure and applied mathematics, engineering, mathematical physics, and signal processing.

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88
Author: Robion C. Kirby
Publisher: Princeton University Press
Total Pages: 368
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400881501

Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Calabi-Yau Varieties: Arithmetic, Geometry and Physics
Author: Radu Laza
Publisher: Springer
Total Pages: 542
Release: 2015-08-27
Genre: Mathematics
ISBN: 1493928309

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.