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The Mathematical Legacy of Srinivasa Ramanujan [[electronic resource] /] / by M. Ram Murty, V. Kumar Murty
| The Mathematical Legacy of Srinivasa Ramanujan [[electronic resource] /] / by M. Ram Murty, V. Kumar Murty |
| Autore | Murty M. Ram |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New Delhi : , : Springer India : , : Imprint : Springer, , 2013 |
| Descrizione fisica | 1 online resource (184 p.) |
| Disciplina | 510.92 |
| Soggetto topico |
Number theory
Mathematics History Combinatorics Special functions Fourier analysis Algebra Number Theory History of Mathematical Sciences Special Functions Fourier Analysis |
| Soggetto genere / forma | History |
| ISBN |
1-283-69784-X
81-322-0770-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Chapter 1. The Legacy of Srinivasa Ramanujan -- Chapter 2. The Ramanujan tau function -- Chapter 3. Ramanujan’s conjecture and l-adic representations -- Chapter 4. The Ramanujan conjecture from GL(2) to GL(n) -- Chapter 5. The circle method -- Chapter 6. Ramanujan and transcendence -- Chapter 7. Arithmetic of the partition function -- Chapter 8. Some nonlinear identities for divisor functions -- Chapter 9. Mock theta functions and mock modular forms -- Chapter 10. Prime numbers and highly composite numbers -- Chapter 11. Probabilistic number theory -- Chapter 12. The Sato-Tate conjecture for the Ramanujan tau-function -- Bibliography -- Index. |
| Record Nr. | UNINA-9910438158403321 |
Murty M. Ram
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| New Delhi : , : Springer India : , : Imprint : Springer, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Problems in the Theory of Modular Forms / / by M. Ram Murty, Michael Dewar, Hester Graves
| Problems in the Theory of Modular Forms / / by M. Ram Murty, Michael Dewar, Hester Graves |
| Autore | Murty M. Ram |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (XVII, 291 p. 8 illus.) |
| Disciplina | 512.74 |
| Collana | IMSc Lecture Notes in Mathematics |
| Soggetto topico |
Number theory
Operator theory Special functions Sequences (Mathematics) Number Theory Operator Theory Special Functions Sequences, Series, Summability |
| ISBN | 981-10-2651-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I Problems -- Chapter 1. Jacobi’s q-series -- Chapter 2. The Modular Group -- Chapter 3. The Upper Half-Plane -- Chapter 4. Modular Forms of Level One -- Chapter 5. The Ramanujan _ T-function -- Chapter 6. Modular Forms of Higher Level -- Chapter 7. The Petersson Inner Product -- Chapter 8. Hecke Operators of Higher Level -- Chapter 9. Dirichlet Series and Modular Forms -- Chapter 10. Special Topics -- Part II Solutions -- Chapter 1. Jacobi’s q-series -- Chapter 2. The Modular Group -- Chapter 3. The Upper Half-Plane -- Chapter 4. Modular Forms of Level One -- Chapter 5. The Ramanujan _ T-function -- Chapter 6. Modular Forms of Higher Level -- Chapter 7. The Petersson Inner Product -- Chapter 8. Hecke Operators of Higher Level -- Chapter 9. Dirichlet Series and Modular Forms -- Chapter 10. Special Topics. |
| Record Nr. | UNINA-9910155526903321 |
|
Murty M. Ram
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| Singapore : , : Springer Singapore : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Transcendental Numbers / / by M. Ram Murty, Purusottam Rath
| Transcendental Numbers / / by M. Ram Murty, Purusottam Rath |
| Autore | Murty M. Ram |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (219 p.) |
| Disciplina | 512.73 |
| Soggetto topico |
Number theory
Algebra Mathematical analysis Number Theory Analysis |
| ISBN | 1-4939-0832-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Liouville’s theorem -- 2. Hermite’s Theorem -- 3. Lindemann’s theorem -- 4. The Lindemann-Weierstrass theorem -- 5. The maximum modulus principle -- 6. Siegel’s lemma -- 7. The six exponentials theorem -- 8. Estimates for derivatives -- 9. The Schneider-Lang theorem -- 10. Elliptic functions -- 11. Transcendental values of elliptic functions -- 12. Periods and quasiperiods -- 13. Transcendental values of some elliptic integrals -- 14. The modular invariant -- 15. Transcendental values of the j-function -- 16. More elliptic integrals -- 17. Transcendental values of Eisenstein series -- 18. Elliptic integrals and hypergeometric series -- 19. Baker’s theorem -- 20. Some applications of Baker’s theorem -- 21. Schanuel’s conjecture -- 22. Transcendental values of some Dirichlet series -- 23. Proof of the Baker-Birch-Wirsing theorem -- 24. Transcendence of some infinite series -- 25. Linear independence of values of Dirichlet L-functions -- 26. Transcendence of values of modular forms -- 27. Transcendence of values of class group L-functions -- 28. Periods, multiple zeta functions and (3). . |
| Record Nr. | UNINA-9910299989203321 |
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Murty M. Ram
|
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| New York, NY : , : Springer New York : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||