Lifting problem for universal quadratic forms
| Autor: | Pavlo Yatsyna, Vítězslav Kala |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Degree (graph theory)
Mathematics - Number Theory General Mathematics 010102 general mathematics 11E12 11E25 11R11 11R18 11H06 11H55 Algebraic number field 01 natural sciences Upper and lower bounds Combinatorics Quadratic form 0103 physical sciences Quadratic field 010307 mathematical physics Ideal (ring theory) 0101 mathematics Real number Mathematics |
| Popis: | We study totally real number fields that admit a universal quadratic form whose coefficients are rational integers. We show that $\mathbb Q(\sqrt 5)$ is the only such real quadratic field, and that among fields of degrees 3, 4, 5, and 7 which have principal codifferent ideal, the only one is $\mathbb Q(\zeta_7+\zeta_7^{-1})$, over which the form $x^2+y^2+z^2+w^2+xy+xz+xw$ is universal. Moreover, we prove an upper bound for Pythagoras numbers of orders in number fields that depends only on the degree of the number field. Comment: 16 pages, incorporated referee comments |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|