A note on -sets.
On the problem
Addendum to “On the problem”
Quadratic congruences on average and rational points on cubic surfaces
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A₅ + A₁.
On Hecke eigenvalues at primes of the form [g(n)]
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].
Bombieri-Vinogradov type theorems for sparse sets of moduli
Automorphisms with exotic orbit growth
The dynamical Mertens' theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compact connected groups with a continuum of growth rates on two different growth scales. This shows in particular that the space of all ergodic algebraic dynamical systems modulo the equivalence of shared orbit-growth asymptotics is not countable. In contrast, for the equivalence relation of measurable isomorphism...
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