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Strongly complete sets and a conjecture of ErdÅs
Steve Fan
The paper proves that a set of natural numbers is strongly complete—still able to represent all large integers as sums of distinct elements after removing finitely many members—und…
The van der Corput property for sums of two squares
Steve Fan, Andrew Lott
Let We prove a power-saving form of the van der Corput property for . As a consequence, we obtain a strong Sá…
Extensions of the Furstenberg-Sárközy theorem via the arithmetic level- inequality
Carlo Francisco E. Adajar, Rishika Agrawal, Mukul Rai Choudhuri +6
Very recently, Green and Sawhney obtained a quasipolynomial bound in the Furstenberg--Sárközy theorem for square differences by proving an ''arithmetic level-'' inequality, th…
Weighted ErdÅs-Kac Theorems via Computing Moments
Steve Fan
By adapting the moment method developed by Granville and Soundararajan [17], Khan, Milinovich and Subedi [24] recently obtained a weighted version of the ErdÅs--Kac theorem for $Ï…
Shifted-prime divisors
Steve Fan, Carl Pomerance
Let denote the number of divisors of that are shifted primes, that is, the number of divisors of of the form , with prime. Studied by Prachar in an influ…