The project investigates classical open questions in number theory such as the twin prime conjecture, which states that there are infinitely many pirme numbers p such that p+2 is also a prime number. This problem has symmetries based on the matrix group GL(2) that have been exploited in previous research. The main goal is to develop a new method based on higher rank matrix groups such as GL(3) and study how these higher rank symmetries may be applied to number theoretical problems such as the equidistribution of roots of entangled quadratic congruences, correlations of the ternary divisor function, and the sixth moment of the zeta function

2025

2029