Tuesday 4 June 2024, 16:00 - 17:00 in HG00.310
Aaron Levin (Michigan State)
Greatest common divisors in Diophantine approximation
In 2003, Bugeaud, Corvaja, and Zannier gave an upper bound for the greatest common divisor \(\mathrm{gcd}(a^n-1,b^n-1)\), where a and b are fixed integers and n varies over the positive integers. In contrast to the elementary statement of their result, the proof required deep results from Diophantine approximation. I will discuss a higher-dimensional generalization of their result and some recent related results.