Thesis (Selection of subject)Thesis (Selection of subject)(version: 285)
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Univerzální kvadratické formy nad řády v číselných tělesech
Thesis title in Czech: Univerzální kvadratické formy nad řády v číselných tělesech
Thesis title in English: Universal quadratic forms over orders in number fields
Academic year of topic announcement: 2017/2018
Type of assignment: dissertation
Thesis language:
Department: Department of Algebra (32-KA)
Supervisor: Mgr. Vítězslav Kala, Ph.D.
Author: hidden - assigned and confirmed by the Study Dept.
Date of registration: 27.09.2018
Date of assignment: 27.09.2018
Confirmed by Study dept. on: 29.10.2018
Guidelines
The goal of the thesis is to study universal and regular quadratic forms over orders in totally real number fields and other closely related topics. Most of the recent research concerning indecomposable integers and the ranks of universal forms has been done only over the maximal order in a real quadratic field. One of the aims of the thesis is to extend these results to general orders. This is closely related to the study of quadratic forms that are assumed to represent only some arithmetic progression of algebraic integers, and to regular quadratic forms.
References
Juergen Neukirch, Algebraic Number Theory, Springer 1999.
Oskar Perron, Die Lehre von den Kettenbruechen, B.G. Teubner, 1913.
David A. Cox, Primes of the Form x^2+ny^2: Fermat, Class Field Theory, and Complex Multiplication, Wiley, 1989.
Wai Kiu Chan and Maria Ines Icaza, Positive definite almost regular ternary quadratic forms over totally real number fields, Bull. London Math. Soc., 40 (2008), 1025-1037.
Valentin Blomer and Vitezslav Kala, Number fields without n-ary universal quadratic forms, Math. Proc. Cambridge Philos. Soc. 159 (2015), no. 2, 239–252.
Vítezslav Kala, Norms of indecomposable integers in real quadratic fields, J. Number Theory 166 (2016), 193-207.
Valentin Blomer and Vitezslav Kala, On the rank of universal quadratic forms over real quadratic fields, Doc. Math. 2018.

 
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