5 papers
Escalations and criteria over real quadratic fields
Jakub Krásenský, Giuliano Romeo
The famous 15-Theorem and 290-Theorem fully characterise universal quadratic forms over . Similar theorems exist for every totally real number field, but only over $\ma…
Universality criterion sets for quadratic forms over number fields
Vitezslav Kala, Jakub Krásenský, Giuliano Romeo
In analogy with the 290-Theorem of Bhargava-Hanke, a criterion set is a finite subset of the totally positive integers in a given totally real number field such that if a quadr…
Representing rational integers by generalized quadratic forms over quadratic fields
OndÅej Chwiedziuk, MatÄj Doležálek, Emma PÄchouÄková +5
We investigate generalized quadratic forms with values in the set of rational integers over quadratic fields. We characterize the real quadratic fields which admit a positive defin…
The arithmetic of continued fractions in the field of -adic numbers
Giuliano Romeo, Giulia Salvatori
Continued fractions have been long studied due to their strong properties, such as rational approximation. In this extent, their arithmetic over real numbers has represented an int…
Real convergence and periodicity of -adic continued fractions
Giuliano Romeo
Continued fractions have been generalized over the field of -adic numbers, where it is still not known an analogue of the famous Lagrange's Theorem. In general, the periodicity…