Difference between revisions of "Math 587: Introduction to Analytic Number Theory."

From MathWiki
Jump to: navigation, search
(Minimal learning outcomes)
(Minimal learning outcomes)
Line 33: Line 33:
 
#*average order of τ(''n''), σ(''n'') and φ(''n'')
 
#*average order of τ(''n''), σ(''n'') and φ(''n'')
 
#'''Elementary theorems on distribution of prime numbers'''
 
#'''Elementary theorems on distribution of prime numbers'''
 +
#*Chebyshev's inequalities
 +
#*Asymptotic formula for :<math>\sum_{p\le x} 1/p</math>
 
</ul>
 
</ul>
  

Revision as of 09:24, 25 May 2010

Catalog Information

Title

Introduction to Analytic Number Theory.

Credit Hours

(3:3:0)

Offered

F

Prerequisite

(Math 352) or equivalent; instructor's consent.

Description

Arithmetical functions; distribution of primes; Dirichlet characters; Dirichlet's theorem; Gauss sums; primitive roots; Dirichlet L-functions; Riemann zeta-function; prime number theorem; partitions.

Desired Learning Outcomes

Students should gain a familiarity with the problems and tools of analytic number theory at beginning graduate level.

Prerequisites

A knowledge of complex analysis at the level of a first course such as Math 352 should suffice.

Minimal learning outcomes

Students should be familiar with the following concepts. They should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving simple results.

    1. Arithmetic functions
      • convolution of arithmetic functions
      • Möbius inversion
      • multiplication function
      • Euler's summation formula, Abel's identity
      • average order of τ(n), σ(n) and φ(n)
    2. Elementary theorems on distribution of prime numbers
      • Chebyshev's inequalities
      • Asymptotic formula for :<math>\sum_{p\le x} 1/p</math>

Additional topics

Courses for which this course is prerequisite