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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On realization of isometries for higher rank quadratic lattices over number fields
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by Wai Kiu Chan and Han Li PDF
Trans. Amer. Math. Soc. 375 (2022), 4619-4640 Request permission

Abstract:

Let $F$ be a number field, and $n\geq 3$ be an integer. In this paper we give an effective procedure which (1) determines whether two given quadratic lattices on $F^n$ are isometric or not, and (2) produces an invertible linear transformation realizing the isometry provided the two given lattices are isometric. A key ingredient in our approach is a search bound for the equivalence of two given quadratic forms over number fields which we prove using methods from algebraic groups, homogeneous dynamics and spectral theory of automorphic forms.
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Additional Information
  • Wai Kiu Chan
  • Affiliation: Department of Mathematics and Computer Science, Wesleyan University, Middletown, Connecticut 06459
  • MR Author ID: 336822
  • ORCID: 0000-0003-2293-0017
  • Email: wkchan@wesleyan.edu
  • Han Li
  • Affiliation: Department of Mathematics and Computer Science, Wesleyan University, Middletown, Connecticut 06459
  • MR Author ID: 1080132
  • Email: hli03@wesleyan.edu
  • Received by editor(s): September 6, 2021
  • Published electronically: April 21, 2022
  • Additional Notes: The second author acknowledges support by the NSF grant DMS #1700109, and the Simons Foundation grant #853671.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 4619-4640
  • MSC (2020): Primary 11E12, 37A44; Secondary 11E20, 37A25
  • DOI: https://doi.org/10.1090/tran/8670
  • MathSciNet review: 4439487