Number fields without universal quadratic forms of small rank exist in most degrees-Reference-Cited by-同舟云学术

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Number fields without universal quadratic forms of small rank exist in most degrees

Published:2022-05-06 Issue:2 Volume:174 Page:225-231
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

KALA VÍTĚZSLAV

Abstract

AbstractWe prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference31 articles.

1. [Su] Sun, L. . A finiteness theorem for quadratic forms. Preprint.

2. [KTZ] Krásenský, J. , Tinková, M. and Zemková, K. . There are no universal ternary quadratic forms over biquadratic fields. Proc. Edinb. Math. Soc. 63 (2020), 861–912.

3. [BK1] Blomer, V. and Kala, V. . Number fields without universal n-ary quadratic forms. Math. Proc. Camb. Phil. Soc. 159 (2015), 239–252.

4. On the Rank of Universal Quadratic Forms over Real Quadratic Fields

5. [Ki] Kim, B. M. . Universal octonary diagonal forms over some real quadratic fields. Comment. Math. Helv. 75 (2000), 410–414.

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