The Equidistribution Of Lattice Shapes Of Rings Of Integers Of Cubic, Quartic, And Quintic Number Fields: An Artist's Rendering

July 13, 2021|
The Equidistribution Of Lattice Shapes Of Rings Of Integers Of Cubic, Quartic, And Quintic Number Fields: An Artist's Rendering by Piper Harron
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Hardcover
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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.
Piper Harron is a faculty member of the University of Hawai''i at MÄnoa Department of Mathematics. In 2016 she received her PhD in mathematics from Princeton University under Manjul Bhargava.
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Title:The Equidistribution Of Lattice Shapes Of Rings Of Integers Of Cubic, Quartic, And Quintic Number Fields: An Artist's Rendering
Format:Hardcover
Product dimensions:9.25 X 6.1 X 0 in
Shipping dimensions:9.25 X 6.1 X 0 in
Published:July 13, 2021
Publisher:Springer-Verlag/Sci-Tech/Trade
Language:English
Appropriate for ages:All ages
ISBN - 13:9783319765310

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