Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Analytic Number Theory Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: i) Basic theory of multiplicative functions, Dirichlet convolutions, sums of multi plicative functions, Euler-Maclaurin summation formula, Dirichlets hyperbola method, the Perron formula and Mellin inversion formula, Poisson summation formula. ii) The Riemman zeta function, analytic continuation, the functional equation, non-vanishing on the line Rs = 1, the zero-free region, the Prime Number Theorem. iii) Dirichlet characters and Dirichlet L-functions, the functional equation, non- vanishing on the line, Dirichlets theorem on primes in arithmetic pro gression, zero-free region, the exceptional zero and the theorems of Landau and Siegel. iv) Time permitting: Introduction to sieve methods, character sums, subconvex bounds of L-functions etc. Suggested Texts : (a) H. Davenport: Multiplicative Number Theory. (b) T. Apostol: Analytic Number Theory. (c) H. Iwaniec and E. Kowalski: Analytic Number Theory. Evaluation:
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Midterm
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