arXiv subjects
Publications and source records attributed to E. Sofos.
Erdős considered the second moment of the gap-counting function of prime divisors in 1946 and proved an upper bound that is not of the right order of magnitude. We prove asymptotics for all moments. Furthermore, we prove a generalisation stating that the gaps between primes $p$ for which there is no $\mathbb{Q}_p$-point on a random variety are Poisson distributed.
Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over $\mathbb{Q}$ that contains a conic defined over $\mathbb{Q}$.
We prove tight estimates for averages of the twisted Hooley $Δ$-function over arbitrary number fields.
For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with integer coefficients.