12 papers
Height lower bounds for elements of highly composite rings
Siu Hang Man, Niclas Technau, Martin Widmer +1
Let be the composite field of all number fields of degree at most . In 2001 Bombieri and Zannier proved that has the Northcott property and…
Lattice point sumsets and asymptotic approximate groups
Arindam Biswas, Pavlo Yatsyna
We establish new quantitative bounds for asymptotic approximate groups arising from finite subsets of lattices and, more generally, semi-linear subsets of abelian groups. Our appro…
The Minimal Degree of Salem Numbers with Negative Trace
Subham Roy, Pavlo Yatsyna
We show that the minimal degree of a Salem number with prescribed negative trace is bounded below by and above by , up to explicit constants and lower-order…
Even better sums of squares over quintic and cyclotomic fields
Vitezslav Kala, Pavlo Yatsyna
We classify all totally real number fields of degree at most 5 that admit a universal quadratic form with rational integer coefficients; in fact, there are none over the previously…
Pythagoras numbers for infinite algebraic fields
Nicolas Daans, Stevan GajoviÄ, Siu Hang Man +1
We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic…
Asymptotics of -universal lattices over number fields
Dayoon Park, Robin Visser, Pavlo Yatsyna +1
We prove an explicit asymptotic formula for the logarithm of the minimal ranks of -universal lattices over the ring of integers of totally real number fields. We also show that,…