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Birkhäuser
Book cover

The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields

An Artist's Rendering

  • Book
  • May 2030

Overview

Authors:
  1. Piper Harron

    1. Department of Mathematics, University of Hawaii at Manoa, Honolulu, USA

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  • Makes recent number theory results accessible to readers at all levels of math experience with its unique structure

  • Reveals the personal thought process behind mathematical research

  • Uses humor and empathy to express and explain formal mathematics

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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Hawaii at Manoa, Honolulu, USA

    Piper Harron

About the author

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

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