02287cam a22002775i 4500001000800000003000900008005001700017008004100034020002400075040001300099041000800112082001700120100002700137245009400164260004700258300003300305490004100338505082600379520064201205650001901847650002101866650002901887650002301916700003501939700003501974TB12448IN-BhIIT20250731144055.0161125s2016    si |||| o    |||| 0|eng    a9789380250724 (PBK)  aIN-BhIIT  aeng04a512.7bMUR/P1 aMurty, M. Ram.eAuthor10aProblems in the theory of modular forms /cby M. Ram Murty, Michael Dewar, Hester Graves.  aNew Delhi :bHindustan Book Agency,c2015.  axv, 291 p. :bill. ;c24 cm.1 aIMSc Lecture Notes in Mathematics; 10 aPart 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.  aThis 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 tau-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. 0aNumber theory. 0aOperator theory. 0aSequences (Mathematics). 0aSpecial functions.1 aDewar, Michael.eJoint author.1 aGraves, Hester.eJoint author.