# Difference between revisions of "Math 687R: Topics in Analytic Number Theory."

From MathWiki

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#Properties of the gamma function. | #Properties of the gamma function. | ||

#Integral functions of order 1. | #Integral functions of order 1. | ||

− | #The infinite products for ξ(''s'') and & | + | #The infinite products for ξ(''s'') and ξ(''s''). |

+ | #Zero free regions for ζ(''s'') and ''L''(''s'', χ). | ||

</ul> | </ul> | ||

## Revision as of 09:02, 25 May 2010

## Contents

## Catalog Information

### Title

Topics in Analytic Number Theory.

### Credit Hours

3

### Prerequisite

Math 352, 487; or equivalents.

### Description

Current topics of research interest.

## Desired Learning Outcomes

Students should gain a familiarity with a particular area of analytic number theory selected by the instructor.

### Prerequisites

A knowledge of complex analysis and a first course in number theory, at the level provided by Math 352, Math 487, should suffice.

### Minimal learning outcomes

These cannot be specified uniquely for a topics course. The following example gives a clear indication of the level of difficulty appropriate to the course. Students should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving results of suitable accessibility.

- Riemann's memoir on the zeta function.
- The functional equation of the L functions.
- Properties of the gamma function.
- Integral functions of order 1.
- The infinite products for ξ(
*s*) and ξ(*s*). - Zero free regions for ζ(
*s*) and*L*(*s*, χ).