1 citations · 1 across the 18 of their papers we have counts for
19 papers
On the exponential sum over squarefree integers
Nicolas Robles, Alexandru Zaharescu, Dirk Zeindler
Let be the Möbius function and . We prove that if , , , and , then \[\bigg|\sum_{n\le N}μ^2(n)e(αn)\bigg|\ll\l…
Self-intersection Points of Billiard Trajectories in a Square with Small Pockets
Anji Dong, Colin Edsey, Shuta Iwai +1
We study the self-intersections of billiard trajectories in a square with small pockets of size removed from its four corners. In particular, we establish an asymptot…
Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures
Debmalya Basak, Anji Dong, Katerina Saettone +1
On the occasion of George Andrews' and Bruce Berndt's combined 170th birthday, we prove two conjectures of Sir Frederick Pollock that are more than 170 years old. In 1843, Pollock…
Erdős-Moser Equation in Arithmetic Progressions
Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu
We consider the Erdős-Moser equation in arithmetic progressions. We prove among other things that when , for any solution to exist, the above sum…
Admissible Pairs: A Variation to Pollock Conjectures
Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu
We introduce a notion of an admissible pair, and prove a variation to Pollock's conjectures on icosahedral and dodecahedral numbers.
Binomial coefficients with divisors avoiding an interval
Hung M. Bui, Slava Naprienko, Kyle Pratt +1
We solve a fifty-year-old conjecture of Erdős and Graham concerning whether the binomial coefficient with must always have a divisor $\l…