MAS 7216 – Krishnaswami Alladi

MWF 6th period (12:50-1:40pm) – LIT 239 – SPRING 2017

INSTRUCTOR:

OFFICE HOURS:

M and W 7th period (1:55 – 2:45 pm) in LIT 304 and

by appointment.

PREREQUISITES:

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

COURSE DESCRIPTION:

This course is a continuation of MAS 7215.

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.

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.

Created by K. Alladi (alladik@ufl.edu) on Tuesday, December 06, 2016.