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1
Content available remote

Addendum to "On the $p^λ$ problem"

100%
Baier S.
Acta Arithmetica
|
2005
|
tom 117
|
nr 2
181-186
2
Content available remote

On the $p^λ$ problem

100%
Baier S.
Acta Arithmetica
|
2004
|
tom 113
|
nr 1
77-101
3
Content available remote

Quadratic congruences on average and rational points on cubic surfaces

64%
Baier S., Derenthal U.
Acta Arithmetica
|
2015
|
tom 171
|
nr 2
145-171
EN
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.
4
Content available remote

Bombieri-Vinogradov type theorems for sparse sets of moduli

64%
Baier S., Zhao L.
Acta Arithmetica
|
2006
|
tom 125
|
nr 2
187-201
5
Content available remote

On Hecke eigenvalues at primes of the form [g(n)]

64%
Baier S., Zhao L.
Acta Arithmetica
|
2013
|
tom 158
|
nr 4
341-357
EN
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)].
6
Content available remote

Automorphisms with exotic orbit growth

51%
Baier S., Jaidee S., Stevens S., Ward T.
Acta Arithmetica
|
2013
|
tom 158
|
nr 2
173-197
EN
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 or equal entropy it is not known if the quotient space is countable or uncountable (this problem is a manifestation of Lehmer's problem).
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