Author: Yasemin Kara
Publisher:
ISBN:
Category :
Languages : en
Pages : 264
Book Description
This thesis concerns the spectral theory of the Laplacian on Riemann surfaces of finite type, with emphasis on the quotients of the upper half plane by congruence subgroups. In a first part we show, following Otal, that on a Riemann surface M of genus g with n punctures there are at most 2g [-] 2 + n eigenvalues [lamda] with [lamda] [LESS-THAN OR EQUAL TO] 1/4. In a second part, we focus on arithmetic surfaces. This subject is treated by Maass in a paper that is difficult to read. We work out some examples of his construction of Maass forms.
The Laplacian on Hyperbolic Riemann Surfaces and Maass Forms
Author: Yasemin Kara
Publisher:
ISBN:
Category :
Languages : en
Pages : 264
Book Description
This thesis concerns the spectral theory of the Laplacian on Riemann surfaces of finite type, with emphasis on the quotients of the upper half plane by congruence subgroups. In a first part we show, following Otal, that on a Riemann surface M of genus g with n punctures there are at most 2g [-] 2 + n eigenvalues [lamda] with [lamda] [LESS-THAN OR EQUAL TO] 1/4. In a second part, we focus on arithmetic surfaces. This subject is treated by Maass in a paper that is difficult to read. We work out some examples of his construction of Maass forms.
Publisher:
ISBN:
Category :
Languages : en
Pages : 264
Book Description
This thesis concerns the spectral theory of the Laplacian on Riemann surfaces of finite type, with emphasis on the quotients of the upper half plane by congruence subgroups. In a first part we show, following Otal, that on a Riemann surface M of genus g with n punctures there are at most 2g [-] 2 + n eigenvalues [lamda] with [lamda] [LESS-THAN OR EQUAL TO] 1/4. In a second part, we focus on arithmetic surfaces. This subject is treated by Maass in a paper that is difficult to read. We work out some examples of his construction of Maass forms.
Representations of Reductive Groups
Author: Avraham Aizenbud
Publisher: American Mathematical Soc.
ISBN: 1470442841
Category : Representations of algebras
Languages : en
Pages : 450
Book Description
This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem. The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope. The themes include representations of p -adic groups and Hecke algebras in all characteristics, representations of real groups and supergroups, theta correspondence, and automorphic forms.
Publisher: American Mathematical Soc.
ISBN: 1470442841
Category : Representations of algebras
Languages : en
Pages : 450
Book Description
This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem. The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope. The themes include representations of p -adic groups and Hecke algebras in all characteristics, representations of real groups and supergroups, theta correspondence, and automorphic forms.
Laplacian Growth on Branched Riemann Surfaces
Author: Björn Gustafsson
Publisher: Springer Nature
ISBN: 3030698637
Category : Mathematics
Languages : en
Pages : 156
Book Description
This book studies solutions of the Polubarinova–Galin and Löwner–Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions have lost their physical meaning due to loss of univalence of the mapping function involved. When the mapping function is no longer locally univalent interesting phase transitions take place, leading to structural changes in the data of the solution, for example new zeros and poles in the case of rational maps. This topic intersects with several areas, including mathematical physics, potential theory and complex analysis. The text will be valuable to researchers and doctoral students interested in fluid dynamics, integrable systems, and conformal field theory.
Publisher: Springer Nature
ISBN: 3030698637
Category : Mathematics
Languages : en
Pages : 156
Book Description
This book studies solutions of the Polubarinova–Galin and Löwner–Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions have lost their physical meaning due to loss of univalence of the mapping function involved. When the mapping function is no longer locally univalent interesting phase transitions take place, leading to structural changes in the data of the solution, for example new zeros and poles in the case of rational maps. This topic intersects with several areas, including mathematical physics, potential theory and complex analysis. The text will be valuable to researchers and doctoral students interested in fluid dynamics, integrable systems, and conformal field theory.
Contributions to the Theory of Riemann Surfaces
Author: Lars Valerian Ahlfors
Publisher: Princeton University Press
ISBN: 0691079390
Category : Mathematics
Languages : en
Pages : 275
Book Description
A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Publisher: Princeton University Press
ISBN: 0691079390
Category : Mathematics
Languages : en
Pages : 275
Book Description
A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Representation Theory, Complex Analysis, and Integral Geometry
Author: Bernhard Krötz
Publisher: Springer Science & Business Media
ISBN: 0817648178
Category : Mathematics
Languages : en
Pages : 282
Book Description
This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
Publisher: Springer Science & Business Media
ISBN: 0817648178
Category : Mathematics
Languages : en
Pages : 282
Book Description
This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
The Spectrum of Hyperbolic Surfaces
Author: Nicolas Bergeron
Publisher: Springer
ISBN: 3319276662
Category : Mathematics
Languages : en
Pages : 375
Book Description
This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
Publisher: Springer
ISBN: 3319276662
Category : Mathematics
Languages : en
Pages : 375
Book Description
This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
Eisenstein Series and Automorphic $L$-Functions
Author: Freydoon Shahidi
Publisher: American Mathematical Soc.
ISBN: 0821849891
Category : Mathematics
Languages : en
Pages : 218
Book Description
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
Publisher: American Mathematical Soc.
ISBN: 0821849891
Category : Mathematics
Languages : en
Pages : 218
Book Description
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
Advances in the Theory of Riemann Surfaces. (AM-66), Volume 66
Author: Lars Valerian Ahlfors
Publisher: Princeton University Press
ISBN: 1400822491
Category : Mathematics
Languages : en
Pages : 433
Book Description
Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.
Publisher: Princeton University Press
ISBN: 1400822491
Category : Mathematics
Languages : en
Pages : 433
Book Description
Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.
Advances in the Theory of Riemann Surfaces
Author: Lars Valerian Ahlfors
Publisher: Princeton University Press
ISBN: 9780691080819
Category : Mathematics
Languages : en
Pages : 436
Book Description
Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.
Publisher: Princeton University Press
ISBN: 9780691080819
Category : Mathematics
Languages : en
Pages : 436
Book Description
Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.
Spectral Geometry
Author: Pierre H. Berard
Publisher: Springer
ISBN: 3540409580
Category : Mathematics
Languages : en
Pages : 284
Book Description
Publisher: Springer
ISBN: 3540409580
Category : Mathematics
Languages : en
Pages : 284
Book Description