03934nam 22006615 450 991015552690332120250609111004.0981-10-2651-310.1007/978-981-10-2651-5(CKB)4340000000027190(DE-He213)978-981-10-2651-5(MiAaPQ)EBC4748776(PPN)197135315(MiAaPQ)EBC6242316(EXLCZ)99434000000002719020161125d2016 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierProblems in the Theory of Modular Forms /by M. Ram Murty, Michael Dewar, Hester Graves1st ed. 2016.Singapore :Springer Singapore :Imprint: Springer,2016.1 online resource (XVII, 291 p. 8 illus.) IMSc Lecture Notes in Mathematics,2509-808X981-10-2650-5 Includes bibliographical references at the end of each chapters and index.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.This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field. .IMSc Lecture Notes in Mathematics,2509-808XNumber theoryOperator theoryFunctions, SpecialSequences (Mathematics)Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Special Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M1221XSequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XNumber theory.Operator theory.Functions, Special.Sequences (Mathematics)Number Theory.Operator Theory.Special Functions.Sequences, Series, Summability.512.74Murty M. Ramauthttp://id.loc.gov/vocabulary/relators/aut61548Dewar Michaelauthttp://id.loc.gov/vocabulary/relators/autGraves Hesterauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910155526903321Problems in the Theory of Modular Forms2124671UNINA