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Modular functions and Dirichlet series in number theory / Tom M. Apostol
| Modular functions and Dirichlet series in number theory / Tom M. Apostol |
| Autore | Apostol, Tom M. |
| Edizione | [2. ed] |
| Pubbl/distr/stampa | New York, : Springer, 1990 |
| Descrizione fisica | XI, 204 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11F03 - Modular and automorphic functions [MSC 2020] 11F67 - Special values of automorphic $L$-series, periods of automorphic forms, cohomology, modular symbols [MSC 2020] |
| Soggetto non controllato |
Analytic Number Theory
Complex Analysis Developments Elliptic functions Fields Functions Knowledge Modular forms Module functions Number theory Partition Riemann zeta functions Shapes Time Zeta functions |
| ISBN | 978-03-87901-85-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0024341 |
Apostol, Tom M.
|
||
| New York, : Springer, 1990 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Modular functions and Dirichlet series in number theory / Tom M. Apostol
| Modular functions and Dirichlet series in number theory / Tom M. Apostol |
| Autore | Apostol, Tom M. |
| Edizione | [2. ed] |
| Pubbl/distr/stampa | New York, : Springer, 1990 |
| Descrizione fisica | xi, 204 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11F03 - Modular and automorphic functions [MSC 2020] 11F67 - Special values of automorphic $L$-series, periods of automorphic forms, cohomology, modular symbols [MSC 2020] |
| Soggetto non controllato |
Analytic Number Theory
Complex Analysis Development Elliptic functions Fields Functions Knowledge Modular forms Module functions Number theory Partition Riemann zeta functions Shapes Time Zeta functions |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00287754 |
|
Apostol, Tom M.
|
||
| New York, : Springer, 1990 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Modular functions and Dirichlet series in number theory / Tom M. Apostol
| Modular functions and Dirichlet series in number theory / Tom M. Apostol |
| Autore | Apostol, Tom M. |
| Edizione | [2. ed] |
| Pubbl/distr/stampa | New York, : Springer, 1990 |
| Descrizione fisica | XI, 204 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11F03 - Modular and automorphic functions [MSC 2020] 11F67 - Special values of automorphic $L$-series, periods of automorphic forms, cohomology, modular symbols [MSC 2020] |
| Soggetto non controllato |
Analytic Number Theory
Complex Analysis Development Elliptic functions Fields Functions Knowledge Modular forms Module functions Number theory Partition Riemann zeta functions Shapes Time Zeta functions |
| ISBN | 978-03-87901-85-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00024341 |
|
Apostol, Tom M.
|
||
| New York, : Springer, 1990 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Modular functions and Dirichlet series in number theory / Tom M. Apostol
| Modular functions and Dirichlet series in number theory / Tom M. Apostol |
| Autore | Apostol, Tom M. |
| Pubbl/distr/stampa | New York, : Springer, 1976 |
| Descrizione fisica | x, 198 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11P81 - Elementary theory of partitions [MSC 2020] 30F35 - Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) [MSC 2020] 11F12 - Automorphic forms, one variable [MSC 2020] 11F03 - Modular and automorphic functions [MSC 2020] 30B50 - Dirichlet series, exponential series and other series in one complex variable [MSC 2020] 11M35 - Hurwitz and Lerch zeta functions [MSC 2020] |
| Soggetto non controllato |
Analytic Number Theory
Complex Analysis Developments Elliptic functions Fields Functions Knowledge Modular forms Module functions Number theory Partition Riemann zeta functions Shapes Time Zeta functions |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0268024 |
|
Apostol, Tom M.
|
||
| New York, : Springer, 1976 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Modular functions and Dirichlet series in number theory / Tom M. Apostol
| Modular functions and Dirichlet series in number theory / Tom M. Apostol |
| Autore | Apostol, Tom M. |
| Pubbl/distr/stampa | New York, : Springer, 1976 |
| Descrizione fisica | x, 198 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11F03 - Modular and automorphic functions [MSC 2020] 11F12 - Automorphic forms, one variable [MSC 2020] 11M35 - Hurwitz and Lerch zeta functions [MSC 2020] 11P81 - Elementary theory of partitions [MSC 2020] 30B50 - Dirichlet series, exponential series and other series in one complex variable [MSC 2020] 30F35 - Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) [MSC 2020] |
| Soggetto non controllato |
Analytic Number Theory
Complex Analysis Development Elliptic functions Fields Functions Knowledge Modular forms Module functions Number theory Partition Riemann zeta functions Shapes Time Zeta functions |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj( r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T. M. A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory. |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00268024 |
|
Apostol, Tom M.
|
||
| New York, : Springer, 1976 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Modular Units / Daniel S. Kubert, Serge Lang
| Modular Units / Daniel S. Kubert, Serge Lang |
| Autore | Kubert, Daniel S. |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1981 |
| Descrizione fisica | xiv, 360 p. : ill. ; 24 cm |
| Altri autori (Persone) | Lang, Serge <1927-2005> |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
14-XX - Algebraic geometry [MSC 2020] 14G25 - Global ground fields [MSC 2020] 11F11 - Holomorphic modular forms of integral weight [MSC 2020] 11R18 - Cyclotomic extensions [MSC 2020] 11G16 - Elliptic and modular units [MSC 2020] |
| Soggetto non controllato |
Arithmetic
Divisor class group Finite Functions Logarithms Modular curves Modular forms Module functions Unit |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0268403 |
|
Kubert, Daniel S.
|
||
| New York, : Springer-Verlag, 1981 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Modular Units / Daniel S. Kubert, Serge Lang
| Modular Units / Daniel S. Kubert, Serge Lang |
| Autore | Kubert, Daniel S. |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1981 |
| Descrizione fisica | xiv, 360 p. : ill. ; 24 cm |
| Altri autori (Persone) | Lang, Serge |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11F11 - Holomorphic modular forms of integral weight [MSC 2020] 11G16 - Elliptic and modular units [MSC 2020] 11R18 - Cyclotomic extensions [MSC 2020] 14-XX - Algebraic geometry [MSC 2020] 14G25 - Global ground fields [MSC 2020] |
| Soggetto non controllato |
Arithmetic
Divisor Class Group Finite Functions Logarithms Modular curves Modular forms Module functions Unit |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C[j] in the function field of X(N) over C. Here j is the classical modular function. However, for arithmetic applications, one considers the curve as defined over the cyclotomic field Q(JlN) of N-th roots of unity, and one takes the integral closure either of Q[j] or Z[j], depending on how much arithmetic one wants to throw in. The units in these rings consist of those modular functions which have no zeros or poles in the upper half plane. The points of X(N) which lie at infinity,that is which do not correspond to points on the above affine set, are called the cusps, because of the way they look in a fundamental domain in the upper half plane. They generate a subgroup of the divisor class group, which turns out to be finite, and is called the cuspidal divisor class group. |
| Record Nr. | UNICAMPANIA-VAN00268403 |
|
Kubert, Daniel S.
|
||
| New York, : Springer-Verlag, 1981 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||