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The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering 2021 Edition
Contributor(s): Harron, Piper (Author)

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 ISBN: 3319765310     ISBN-13: 9783319765310
Publisher: Birkhauser
OUR PRICE: $103.55  

Binding Type: Hardcover
Published: June 2025
This item may be ordered no more than 25 days prior to its publication date of June 13, 2025
Additional Information
BISAC Categories:
- Mathematics | Number Theory
- Mathematics | Algebra - Abstract
- Mathematics | Logic
Dewey: 511.33
 
Descriptions, Reviews, Etc.
Publisher Description:
This book seeks to explain the author's joint work with Manjul Bhargava in a fun and accessible way. On its face, the subject matter concerns properties of number fields, namely the shape (literally and mathematically) of their rings of integers. The result says essentially that the ring of integers of a random number field should not have any special symmetries when viewed as a lattice in real space. The proof requires a parametrization, a counting method, an understanding of conditions mod p, a way to isolate the things we actually want to count, and a volume calculation. This has all been presented to the experts in an eleven page paper. The real purpose of this book, then, is not to present the results and the proof, but to really attempt to explain not just the math but also the struggles, that go into the result.
 
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