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The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering
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The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering (Hardback)

£79.00
Pre-order for despatch on publication.

Synopsis

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.

Science & MathematicsMathematicsAlgebraScience & MathematicsMathematicsNumber theory Publisher: Birkhauser Verlag AG Publication Date: 13/06/2021 ISBN-13: 9783319765310  Details: Type: Hardback Format: Books
Availability: Pre-order for despatch on publication. Pre-Order

Piper Harron is a faculty member of the University of Hawai'i at Manoa Department of Mathematics. In 2016 she received her PhD in mathematics from Princeton University under Manjul Bhargava.

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