Slicing the stars: counting algebraic numbers

Cite

Related Material

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Gunther, Joseph

Formal Metadata

Title

Slicing the stars: counting algebraic numbers

Title of Series

Rational and Integral Points via Analytic and Geometric Methods (18w5012)

Number of Parts

Author

Gunther, Joseph

Contributors

Grizzard, Robert

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/58362 (DOI)

Publisher

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Release Date

2018

Language

English

Content Metadata

Subject Area

Mathematics

Genre

Workshop/Interactive Format Lecture

Abstract

Masser and Vaaler gave an asymptotic formula for the number of algebraic numbers of given degree and increasing height. This problem was solved by counting lattice points in an expanding star body. We'll explain how to estimate the volumes of slices of star bodies, which allows one to count algebraic integers, algebraic integers of given norm and/or trace, and more. There will be pictures.