18 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…
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,…
Counting polynomials with positive roots
Pavlo Yatsyna, Błażej Żmija
This paper investigates the number of monic integer polynomials of degree whose roots are all real and positive. We establish an asymptotic formula for the case of fixed trace…
Pythagoras numbers for infinite algebraic fields
Nicolas Daans, Stevan Gajović, 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…