9780821844885 - modular functions in analytic number theory di knopp, marvin i. (5 risultati)
Lingua: Inglese
Editore: American Mathematical Society, 2008
- Rilegato
Da: Revaluation Books, Exeter, Regno UnitoRevaluation Books
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 52,68
EUR 11,67 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 1 disponibili
Hardcover. Condizione: Brand New. 2nd edition. 154 pages. 9.20x6.20x0.60 inches. In Stock.
Lingua: Inglese
Editore: American Mathematical Society, US, 2002
- Rilegato
Da: Rarewaves.com USA, London, LONDO, Regno UnitoRarewaves.com USA
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 69,27
Spedizione gratuitaSpedito da Regno Unito a U.S.A.Quantità: 1 disponibili
Hardback. Condizione: New. Second Edition. Knopp's engaging book presents an introduction to modular functions in number theory by concentrating on two modular functions, $\eta(\tau)$ and $\vartheta(\tau)$, and their applications to two number-theoretic functions, $p(n)$ and $r_s(n)$. They are well chosen, as at the heart of the…se particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching significance with important connections to a great many fields of mathematics. The book is essentially self-contained, assuming only a good first-year course in analysis. The excellent exposition presents the beautiful interplay between modular forms and number theory, making the book an excellent introduction to analytic number theory for a beginning graduate student. Table of Contents: The Modular Group and Certain Subgroups: 1. The modular group; 2. A fundamental region for $\Gamma(1)$; 3. Some subgroups of $\Gamma(1)$; 4. Fundamental regions of subgroups. Modular Functions and Forms: 1. Multiplier systems; 2. Parabolic points; 3 Fourier expansions; 4. Definitions of modular function and modular form; 5. Several important theorems. The Modular Forms $\eta(\tau)$ and $\vartheta(\tau)$: 1. The function $\eta(\tau)$; 2. Several famous identities; 3. Transformation formulas for $\eta(\tau)$; 4. The function $\vartheta(\tau)$. The Multiplier Systems $\upsilon_{\eta}$ and $\upsilon_{\vartheta}$: 1. Preliminaries; 2. Proof of theorem 2; 3. Proof of theorem 3. Sums of Squares: 1. Statement of results; 2. Lipschitz summation formula; 3. The function $\psi_s(\tau)$; 4. The expansion of $\psi_s(\tau)$ at $-1$; 5. Proofs of theorems 2 and 3; 6. Related results. The Order of Magnitude of $p(n)$: 1. A simple inequality for $p(n)$; 2. The asymptotic formula for $p(n)$; 3. Proof of theorem 2. The Ramanujan Congruences for $p(n)$: 1. Statement of the congruences; 2. The functions $\Phi_{p,r}(\tau)$ and $h_p(\tau)$; 3. The function $s_{p, r}(\tau)$; 4. The congruence for $p(n)$ Modulo 11; 5. Newton's formula; 6. The modular equation for the prime 5; 7. The modular equation for the prime 7. Proof of the Ramanujan Congruences for Powers of 5 and 7: 1. Preliminaries; 2. Application of the modular equation; 3. A digression: The Ramanujan identities for powers of the prime 5; 4. Completion of the proof for powers of 5; 5. Start of the proof for powers of 7; 6. A second digression: The Ramanujan identities for powers of the prime 7; 7. Completion of the proof for powers of 7. Index. (CHEL/337.H).
Lingua: Inglese
Editore: American Mathematical Society, 2008
- Rilegato
Da: Kennys Bookshop and Art Galleries Ltd., Galway, GY, IrlandaKennys Bookshop and Art Galleries Ltd.
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 66,03
EUR 9,50 spedizioneSpedito da Irlanda a U.S.A.Quantità: 1 disponibili
Condizione: New. Series: AMS Chelsea Publishing. Num Pages: 154 pages, illustrations. BIC Classification: PBH. Category: (P) Professional & Vocational. Dimension: 157 x 234 x 12. Weight in Grams: 358. . 2008. 2nd Revised edition. Hardcover. . . . .
Lingua: Inglese
Editore: American Mathematical Society, 2008
- Rilegato
Da: Kennys Bookstore, Olney, MD, U.S.A.Kennys Bookstore
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 80,36
EUR 8,98 spedizioneSpedito in U.S.A.Quantità: 1 disponibili
Condizione: New. Series: AMS Chelsea Publishing. Num Pages: 154 pages, illustrations. BIC Classification: PBH. Category: (P) Professional & Vocational. Dimension: 157 x 234 x 12. Weight in Grams: 358. . 2008. 2nd Revised edition. Hardcover. . . . . Books ship from the US and Ireland.
Lingua: Inglese
Editore: American Mathematical Society, US, 2002
- Rilegato
Da: Rarewaves.com UK, London, Regno UnitoRarewaves.com UK
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 65,02
EUR 75,88 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 1 disponibili
Hardback. Condizione: New. Second Edition. Knopp's engaging book presents an introduction to modular functions in number theory by concentrating on two modular functions, $\eta(\tau)$ and $\vartheta(\tau)$, and their applications to two number-theoretic functions, $p(n)$ and $r_s(n)$. They are well chosen, as at the heart of the…se particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching significance with important connections to a great many fields of mathematics. The book is essentially self-contained, assuming only a good first-year course in analysis. The excellent exposition presents the beautiful interplay between modular forms and number theory, making the book an excellent introduction to analytic number theory for a beginning graduate student. Table of Contents: The Modular Group and Certain Subgroups: 1. The modular group; 2. A fundamental region for $\Gamma(1)$; 3. Some subgroups of $\Gamma(1)$; 4. Fundamental regions of subgroups. Modular Functions and Forms: 1. Multiplier systems; 2. Parabolic points; 3 Fourier expansions; 4. Definitions of modular function and modular form; 5. Several important theorems. The Modular Forms $\eta(\tau)$ and $\vartheta(\tau)$: 1. The function $\eta(\tau)$; 2. Several famous identities; 3. Transformation formulas for $\eta(\tau)$; 4. The function $\vartheta(\tau)$. The Multiplier Systems $\upsilon_{\eta}$ and $\upsilon_{\vartheta}$: 1. Preliminaries; 2. Proof of theorem 2; 3. Proof of theorem 3. Sums of Squares: 1. Statement of results; 2. Lipschitz summation formula; 3. The function $\psi_s(\tau)$; 4. The expansion of $\psi_s(\tau)$ at $-1$; 5. Proofs of theorems 2 and 3; 6. Related results. The Order of Magnitude of $p(n)$: 1. A simple inequality for $p(n)$; 2. The asymptotic formula for $p(n)$; 3. Proof of theorem 2. The Ramanujan Congruences for $p(n)$: 1. Statement of the congruences; 2. The functions $\Phi_{p,r}(\tau)$ and $h_p(\tau)$; 3. The function $s_{p, r}(\tau)$; 4. The congruence for $p(n)$ Modulo 11; 5. Newton's formula; 6. The modular equation for the prime 5; 7. The modular equation for the prime 7. Proof of the Ramanujan Congruences for Powers of 5 and 7: 1. Preliminaries; 2. Application of the modular equation; 3. A digression: The Ramanujan identities for powers of the prime 5; 4. Completion of the proof for powers of 5; 5. Start of the proof for powers of 7; 6. A second digression: The Ramanujan identities for powers of the prime 7; 7. Completion of the proof for powers of 7. Index. (CHEL/337.H).
