Author: Richard Bellman
Publisher: Courier Corporation
ISBN: 0486492958
Category : Mathematics
Languages : en
Pages : 100
Book Description
Originally published: New York: Rinehart and Winston, 1961.
A Brief Introduction to Theta Functions
Author: Richard Bellman
Publisher: Courier Corporation
ISBN: 0486492958
Category : Mathematics
Languages : en
Pages : 100
Book Description
Originally published: New York: Rinehart and Winston, 1961.
Publisher: Courier Corporation
ISBN: 0486492958
Category : Mathematics
Languages : en
Pages : 100
Book Description
Originally published: New York: Rinehart and Winston, 1961.
Theta Mathematics
Author: David Barton
Publisher:
ISBN: 9781442549487
Category : Mathematics
Languages : en
Pages : 577
Book Description
Publisher:
ISBN: 9781442549487
Category : Mathematics
Languages : en
Pages : 577
Book Description
Abelian Varieties, Theta Functions and the Fourier Transform
Author: Alexander Polishchuk
Publisher: Cambridge University Press
ISBN: 0521808049
Category : Mathematics
Languages : en
Pages : 308
Book Description
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Publisher: Cambridge University Press
ISBN: 0521808049
Category : Mathematics
Languages : en
Pages : 308
Book Description
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Theta Functions
Author: Maruti Ram Murty
Publisher: American Mathematical Soc.
ISBN: 9780821870112
Category : Mathematics
Languages : en
Pages : 188
Book Description
This book contains lectures on theta functions written by experts well known for excellence in exposition. The lectures represent the content of four courses given at the Centre de Recherches Mathematiques in Montreal during the academic year 1991-1992, which was devoted to the study of automorphic forms. Aimed at graduate students, the book synthesizes the classical and modern points of view in theta functions, concentrating on connections to number theory and representation theory. An excellent introduction to this important subject of current research, this book is suitable as a text in advanced graduate courses.
Publisher: American Mathematical Soc.
ISBN: 9780821870112
Category : Mathematics
Languages : en
Pages : 188
Book Description
This book contains lectures on theta functions written by experts well known for excellence in exposition. The lectures represent the content of four courses given at the Centre de Recherches Mathematiques in Montreal during the academic year 1991-1992, which was devoted to the study of automorphic forms. Aimed at graduate students, the book synthesizes the classical and modern points of view in theta functions, concentrating on connections to number theory and representation theory. An excellent introduction to this important subject of current research, this book is suitable as a text in advanced graduate courses.
Theta Functions on Riemann Surfaces
Author: J. D. Fay
Publisher: Springer
ISBN: 3540378154
Category : Mathematics
Languages : en
Pages : 142
Book Description
These notes present new as well as classical results from the theory of theta functions on Riemann surfaces, a subject of renewed interest in recent years. Topics discussed here include: the relations between theta functions and Abelian differentials, theta functions on degenerate Riemann surfaces, Schottky relations for surfaces of special moduli, and theta functions on finite bordered Riemann surfaces.
Publisher: Springer
ISBN: 3540378154
Category : Mathematics
Languages : en
Pages : 142
Book Description
These notes present new as well as classical results from the theory of theta functions on Riemann surfaces, a subject of renewed interest in recent years. Topics discussed here include: the relations between theta functions and Abelian differentials, theta functions on degenerate Riemann surfaces, Schottky relations for surfaces of special moduli, and theta functions on finite bordered Riemann surfaces.
Eta Products and Theta Series Identities
Author: Günter Köhler
Publisher: Springer Science & Business Media
ISBN: 3642161529
Category : Mathematics
Languages : en
Pages : 627
Book Description
This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. The book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Nevertheless, some theoretical background material is presented that is important for understanding the examples in Part II of the book. In Part I relevant definitions and essential theorems -- such as a complete proof of the structure theorems for coprime residue class groups in quadratic number fields that are not easily accessible in the literature -- are provided. Another example is a thorough description of an algorithm for listing all eta products of given weight and level, together with proofs of some results on the bijection between these eta products and lattice simplices.
Publisher: Springer Science & Business Media
ISBN: 3642161529
Category : Mathematics
Languages : en
Pages : 627
Book Description
This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. The book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Nevertheless, some theoretical background material is presented that is important for understanding the examples in Part II of the book. In Part I relevant definitions and essential theorems -- such as a complete proof of the structure theorems for coprime residue class groups in quadratic number fields that are not easily accessible in the literature -- are provided. Another example is a thorough description of an algorithm for listing all eta products of given weight and level, together with proofs of some results on the bijection between these eta products and lattice simplices.
The Greek Qabalah
Author: Kieren Barry
Publisher: Weiser Books
ISBN: 1609252276
Category : Religion
Languages : en
Pages : 316
Book Description
This book will be of interest to a wide range of readers, from students of Ancient History and early Christianity, to Qabalists and modern magicians. Extensive notes and citations from original sources will make this authoritative work an essential reference for researchers and practitioners for years to come. Includes are appendices for tables of alphabetic symbolism, a list of authors, and a numeric dictionary of Greek words, which represents the largest collection of gematria in print.
Publisher: Weiser Books
ISBN: 1609252276
Category : Religion
Languages : en
Pages : 316
Book Description
This book will be of interest to a wide range of readers, from students of Ancient History and early Christianity, to Qabalists and modern magicians. Extensive notes and citations from original sources will make this authoritative work an essential reference for researchers and practitioners for years to come. Includes are appendices for tables of alphabetic symbolism, a list of authors, and a numeric dictionary of Greek words, which represents the largest collection of gematria in print.
Theta Constants, Riemann Surfaces and the Modular Group
Author: Hershel M. Farkas
Publisher: American Mathematical Soc.
ISBN: 0821813927
Category : Mathematics
Languages : en
Pages : 557
Book Description
There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for number-theoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. Theta functions are also classically connected with Riemann surfaces and with the modular group $\Gamma = \mathrm{PSL (2,\mathbb{Z )$, which provide another path for insights into number theory. Farkas and Kra, well-known masters of the theory of Riemann surfaces and the analysis of theta functions, uncover here interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. For instance, the authors use this approach to derive congruences discovered by Ramanujan for the partition function, with the main ingredient being the construction of the same function in more than one way. The authors also obtain a variant on Jacobi's famous result on the number of ways that an integer can be represented as a sum of four squares, replacing the squares by triangular numbers and, in the process, obtaining a cleaner result. The recent trend of applying the ideas and methods of algebraic geometry to the study of theta functions and number theory has resulted in great advances in the area. However, the authors choose to stay with the classical point of view. As a result, their statements and proofs are very concrete. In this book the mathematician familiar with the algebraic geometry approach to theta functions and number theory will find many interesting ideas as well as detailed explanations and derivations of new and old results. Highlights of the book include systematic studies of theta constant identities, uniformizations of surfaces represented by subgroups of the modular group, partition identities, and Fourier coefficients of automorphic functions. Prerequisites are a solid understanding of complex analysis, some familiarity with Riemann surfaces, Fuchsian groups, and elliptic functions, and an interest in number theory. The book contains summaries of some of the required material, particularly for theta functions and theta constants. Readers will find here a careful exposition of a classical point of view of analysis and number theory. Presented are numerous examples plus suggestions for research-level problems. The text is suitable for a graduate course or for independent reading.
Publisher: American Mathematical Soc.
ISBN: 0821813927
Category : Mathematics
Languages : en
Pages : 557
Book Description
There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for number-theoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. Theta functions are also classically connected with Riemann surfaces and with the modular group $\Gamma = \mathrm{PSL (2,\mathbb{Z )$, which provide another path for insights into number theory. Farkas and Kra, well-known masters of the theory of Riemann surfaces and the analysis of theta functions, uncover here interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. For instance, the authors use this approach to derive congruences discovered by Ramanujan for the partition function, with the main ingredient being the construction of the same function in more than one way. The authors also obtain a variant on Jacobi's famous result on the number of ways that an integer can be represented as a sum of four squares, replacing the squares by triangular numbers and, in the process, obtaining a cleaner result. The recent trend of applying the ideas and methods of algebraic geometry to the study of theta functions and number theory has resulted in great advances in the area. However, the authors choose to stay with the classical point of view. As a result, their statements and proofs are very concrete. In this book the mathematician familiar with the algebraic geometry approach to theta functions and number theory will find many interesting ideas as well as detailed explanations and derivations of new and old results. Highlights of the book include systematic studies of theta constant identities, uniformizations of surfaces represented by subgroups of the modular group, partition identities, and Fourier coefficients of automorphic functions. Prerequisites are a solid understanding of complex analysis, some familiarity with Riemann surfaces, Fuchsian groups, and elliptic functions, and an interest in number theory. The book contains summaries of some of the required material, particularly for theta functions and theta constants. Readers will find here a careful exposition of a classical point of view of analysis and number theory. Presented are numerous examples plus suggestions for research-level problems. The text is suitable for a graduate course or for independent reading.
Tata Lectures on Theta I
Author: David Mumford
Publisher: Springer Science & Business Media
ISBN: 0817645772
Category : Mathematics
Languages : en
Pages : 248
Book Description
This volume is the first of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).
Publisher: Springer Science & Business Media
ISBN: 0817645772
Category : Mathematics
Languages : en
Pages : 248
Book Description
This volume is the first of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).
Handbook of Mathematical Functions
Author: Milton Abramowitz
Publisher: Courier Corporation
ISBN: 9780486612720
Category : Mathematics
Languages : en
Pages : 1068
Book Description
An extensive summary of mathematical functions that occur in physical and engineering problems
Publisher: Courier Corporation
ISBN: 9780486612720
Category : Mathematics
Languages : en
Pages : 1068
Book Description
An extensive summary of mathematical functions that occur in physical and engineering problems