5 papers
Counting principal ideals of small norm in the simplest cubic fields
Mikuláš Zindulka
We estimate the number of principal ideals of norm in the family of the simplest cubic fields. The advantage of our result is that it provides the co…
No proper generalized quadratic forms are universal over quadratic fields
Ondřej Chwiedziuk, Matěj Doležálek, Simona Hlavinková +5
We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be…
Sums of Hurwitz class numbers, CM modular forms, and primes of the form
Mikuláš Zindulka
We consider sums of Hurwitz class numbers of the type , where is composite. For and , we show that these sums can be expressed in…
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…
The Six-Vertex Model with a Non-Standard Boundary Condition
Matěj Doležálek, Martin Raška, Ester Sgallová +2
We consider the enumeration of states in the Brubaker-Bump-Friedberg six-vertex model, whose boundary conditions are determined by an integer partition. In general, we find the num…