Vorlesungen Uber Die Theorie For Elliptischen Modulfunctionen
Vorlesungen Uber Die Theorie For Elliptischen Modulfunctionen

Author: Dr Robert Fricke

Publisher: Legare Street Press

Published: 2023-07-18

Total Pages: 0

ISBN-13: 9781019616581

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Fricke's groundbreaking study of the theory of elliptic modular functions is a must-read for anyone interested in the foundations of modern mathematics. With clear explanations and insightful examples, Fricke offers a comprehensive overview of this complex and fascinating subject. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Some Applications of Modular Forms
Some Applications of Modular Forms

Author: Peter Sarnak

Publisher: Cambridge University Press

Published: 1990-11-15

Total Pages: 124

ISBN-13: 1316582442

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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.

The Evanston Colloquium
The Evanston Colloquium

Author: Felix Klein

Publisher:

Published: 1893

Total Pages: 154

ISBN-13:

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I. Clebsch.--II-III. Sophus Lie.--IV. On the real shape of algebraic curves and surfaces.--V. Theory of functions and geometry.--VI. On the mathematical character of space-intuition, and the relation of pure mathematics to the applied sciences.--VII. The transcendency of the numbers [Greek letter epsilon] and [Greek letter pi].--VII. Ideal numbers.--IX. The solution of higher algebraic equations.--X. On some recent advances in hyperelliptic and Abelian functions.--XI. The most recent researches in non-Euclidean geometry.--XII. The study of mathematics at Göttingen.--Appendix.

Representations of Integers as Sums of Squares
Representations of Integers as Sums of Squares

Author: E. Grosswald

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 262

ISBN-13: 1461385660

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During the academic year 1980-1981 I was teaching at the Technion-the Israeli Institute of Technology-in Haifa. The audience was small, but con sisted of particularly gifted and eager listeners; unfortunately, their back ground varied widely. What could one offer such an audience, so as to do justice to all of them? I decided to discuss representations of natural integers as sums of squares, starting on the most elementary level, but with the inten tion of pushing ahead as far as possible in some of the different directions that offered themselves (quadratic forms, theory of genera, generalizations and modern developments, etc.), according to the interests of the audience. A few weeks after the start of the academic year I received a letter from Professor Gian-Carlo Rota, with the suggestion that I submit a manuscript for the Encyclopedia of Mathematical Sciences under his editorship. I answered that I did not have a ready manuscript to offer, but that I could use my notes on representations of integers by sums of squares as the basis for one. Indeed, about that time I had already started thinking about the possibility of such a book and had, in fact, quite precise ideas about the kind of book I wanted it to be.

Lipman Bers, a Life in Mathematics
Lipman Bers, a Life in Mathematics

Author: Linda Keen

Publisher: American Mathematical Soc.

Published: 2015-09-15

Total Pages: 362

ISBN-13: 1470420562

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The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysis--quasiconformal mappings and moduli of Riemann surfaces--and the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture. The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grand-students, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time.