1 citations · 1 across the 7 of their papers we have counts for
8 papers
Lattice points close to a smooth curve and squarefull numbers in short intervals. II
Ognian Trifonov
By applying recent estimates on the number of integer solutions of ternary quadratic forms in boxes due to Browning and Heath-Brown, we obtain new estimates for the number of latti…
Integer Sequences which Are Closed with Respect to Multiplication and whose Sumset does not Intersect the Sequence
Georgi Demirov, Ognian Trifonov
We investigate increasing sequences of integers with the property that the product of every two terms of the sequence is also a term of the sequence and the sum of every two terms…
Covering systems where the prime divisors of all moduli are only , , or
Joshua Harrington, Jonah Klein, Joshua Lowrance +1
We try to find all quadruples of positive integers with such that there exists a distinct covering system with minimum modulus and least common mu…
Lattice points close to a helix
Jack Dalton, Ognian Trifonov
We obtain lower bound for the maximum distance between any three distinct points in an affine lattice which are close to a helix with small curvature and torsion.
Representing positive integers as a sum of a squarefree number and a small prime
Ognian Trifonov, Jack Dalton
We prove that every positive integer which is not equal to , , , , , , , or can be represented as a sum of a squarefree number and a prime not ex…
An upper bound for the minimum modulus in a covering system with squarefree moduli
Maria Cummings, Michael Filaseta, Ognian Trifonov
Based on work of P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba, we show that if a covering system has distinct squarefree moduli, then the minimum modulus is at…
Bounding the number of lattice points near a convex curve by curvature
Ralph Howard, Ognian Trifonov
We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of o…
Extreme Covering Systems of the Integers
Jack Dalton, Ognian Trifonov
It is proved that if the least modulus of a distinct covering system is 4, its largest modulus is at least 60; also if the least modulus is 3, the LCM of the moduli is at least 120…