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math.NT2024
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…
math.NT2024
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…
math.NT2024
Representing rational integers by generalized quadratic forms over quadratic fields
Ondřej Chwiedziuk, Matěj Doležálek, Emma Pěchoučková +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…