Factors of a perfect square
We consider a conjecture of Erdős and Rosenfeld and a conjecture of Ruzsa when the number is a perfect square. In particular, we show that every perfect square n can have at most five divisors between and .
Lower order terms of the second moment of S(t)
Finding almost squares
More precise Pair Correlation Conjecture on the zeros of the Riemann zeta function
Pair correlation of the zeros of the Riemann zeta function in longer ranges
On the concentration of points on modular hyperbolas and exponential curves
Visible Points on Modular Exponential Curves
We obtain an asymptotic formula for the number of visible points (x,y), that is, with gcd(x,y) = 1, which lie in the box [1,U] × [1,V] and also belong to the exponential modular curves . Among other tools, some recent results of additive combinatorics due to J. Bourgain and M. Z. Garaev play a crucial role in our argument.
Distribution of difference between inverses of consecutive integers modulo .
Finding almost squares. II.
A short note on the difference between inverses of consecutive integers modulo .
Finding almost squares. V.
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