MAS 7215 – Analytic Number Theory I – Fall 2016






MWF 6th period (12:50-1:40pm) – LIT 233 – FALL 2016


INSTRUCTOR:



    Krishnaswami Alladi

    304 Little Hall

    (352) 294-2290
    email: alladik@ufl.edu


OFFICE HOURS:


M and W 8th period (3:00 – 3:50 pm) in LIT 304 and
by appointment.


PREREQUISITES:


Undergraduate course in number theory and a course in complex variable theory


COURSE DESCRIPTION:


Number Theory is one of the two oldest subjects in mathematics, the other being geometry.
Yet, Number Theory is one of the most important and active areas of research today.
Analytic number theory deals with fundamental arithmetical questions which can be tackled
using analytic techniques. The subject has a wealth of outstanding open problems. In the
past decade some dramatic advances have been made on some of these famous problems.
The course will start from scratch and will be self contained, but will reach great heights
in a steady ascent. Topics to be covered will include (and not necessarily in the order
given below): estimates involving prime numbers, arithmetical (number theoretic) functions
– their algebra and asymptotic estimates concerning them, Dirichlet series, the Riemann zeta
function, the prime number theorem and its proof(s), Dirichlet’s theorem on primes in
progressions, the Siegel-Walfisz strongform of the Prime Number Theorem for Arithmetic
Progressions, introduction to sieve methods to understand the prime twins and Goldbach
conjectures – important partial results towards these conjectures, The Erdos-Kac Theorem
in Probabilistic Number Theory.

NOTE: Naturally some of these topics will be covered in MAS 7216.

TEXT:


No assigned text. I will use my own notes. A number of texts will be given as
references. All I expect is a background in complex variable theory.

 

GRADING:


Grades will be based on a few homework assignments,
and seminars that students will have an opportunity to give.


ACCOMODATION FOR STUDENTS WITH DISABILITIES:


Students requesting classroom accommodation must first register with the Dean of
Students Office. The Dean of Students Office will provide documentation to the
student who must then provide this documentation to the Instructor when requesting
accommodation.