Analytic Number Theory, MATH-UA.394.001, Spring, 2017

Assignments, exams, grading

The final grade will be based on weekly homework assignments, a quiz, midterm exam, and a final exam. Assignments will be given each week and due in class, on paper, at the beginning of the following class. There will be a moderate penalty for late homework. Students are allowed but not encouraged to typeset answers.

Communication and announcements

Announcements and most course communication will be done on the course page at the NYU Classes site. This site has a class message board that everyone in the class can see. If you have a technical question or comment, please post it there rather than sending an email to the instructor That way everyone has the same information. Please feel free to contribute. You can check your grades here.

Academic integrity (cheating)

The NYU academic integrity policies. apply to this class. Students may work together but each student must write her/his answers individually. Students may not hand in work they have copied from another source.

Schedule (subject to change)

week topics due
1 Introduction, prime factorization, the Riemann zeta function
2 Infinite products, the Euler product formula Homework 1 due
3 The discrete Fourier transform, modular multiplication, Euler phi function Homework 2 due
4 Finite abelian groups, Dirichlet characters, L functions Homework 3 due
5 Dirichlet theorem (conclusion), Calculus of complex functions, the complex derivative and contour integral Homework 4 due
6 Cauchy residue theorem and properties of complex analytic functions Homework 5 due
7 Cauchy residue theorem for inverting generating functions and Dirichlet series Homework 6 due
Midterm exam
8 Fourier series, the Fourier integral, and the Poisson summation formula Homework 7 due
9 Applications of the Poisson summation formula: sums 1/n^{2p}, Jacobi identity, error bound for lattice points in a circle Homework 8 due
10 Proof of the prime number theorem Homework 9 due
11 Properties of the Riemann zeta function, the functional equation Homework 10 due
12 Partitions, basic properties, product form of the generating function Homework 11 due
13 Asymptotic estimate of the number of partitions Homework 12 due
14 Final Exam