Course Archives Theoretical Statistics and Mathematics Unit
Course: Analytic Number Theory
Level: Postgraduate
Time: Currently not offered
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:
Midterm Exam 30 marks
Home Work / Assignment 20 marks
Final Exam 50 marks
Total 100 marks

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Past Exams
Midterm
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