Displaying similar documents to “A localization theorem in the theory of diophantine approximation and an application to Pell's equation”

A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs

Viviane Baladi, Aïcha Hachemi (2008)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

For large , we consider the ordinary continued fraction of =/ with 1≤≤≤, or, equivalently, Euclid’s gcd algorithm for two integers 1≤≤≤, putting the uniform distribution on the set of and s. We study the distribution of the total cost of execution of the algorithm for an additive cost function on the set ℤ of possible digits, asymptotically for →∞. If is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named...

On sums of Hecke series in short intervals

Aleksandar Ivić (2001)

Journal de théorie des nombres de Bordeaux

Similarity:

We have ∑ K - G ≤ k j ≤ K + G α j H j 3 ( 1 2 ) ≪ ϵ G K 1 + ϵ for K ϵ ≤ G ≤ K , where α j = ρ j ( 1 ) 2 ( cosh π k j ) - 1 , and ρ j ( 1 ) is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue λ j = k j 2 + 1 4 to which the Hecke series H j ( s ) is attached. This result yields the new bound H j ( 1 2 ≪ ϵ k j 1 3 + ϵ .