The distribution of spacings between quadratic residues, II
TLDR
In this article, the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity was studied, and it was shown that the spacing distribution for square free Q is Poissonian.Abstract:
We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for square free Q is Poissonian, this paper extends the result to arbitrary Q.read more
Citations
More filters
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications. Volume II By William Feller. Pp. xviii, 626. 90s. 1966. (Wiley)
Journal ArticleDOI
Divergent square averages
TL;DR: In this paper, it was shown that the sequence of f 2 g 1D1 is L 1 -universally bad, which implies that it is not true that given a dynamical system.X;U;;T/ andf 2L 1./, the ergodic means
Posted Content
Divergent Square Averages
TL;DR: In this article, it was shown that the sequence of f 2 g 1D1 is L 1 -universally bad, which implies that it is not true that given a dynamical system.X;U;;T/ andf 2L 1./, the ergodic means
Book ChapterDOI
Quadratic Residues and Non-Residues in Arithmetic Progression
TL;DR: In this article, the authors studied the problem of detecting long sequences of residues and non-residues in arithmetic progressions, and they used the Dirichlet-Hilbert trick to detect long sets of residues.
Posted Content
Poisson statistics via the Chinese remainder theorem
Andrew Granville,Pär Kurlberg +1 more
TL;DR: In this article, the authors consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the Chinese remainder theorem.
References
More filters
Book
A course in combinatorics
J.H. van Lint,Richard M. Wilson +1 more
TL;DR: The second edition of a popular book on combinatorics as discussed by the authors is a comprehensive guide to the whole of the subject, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes.
Book
An Introduction to the Geometry of Numbers
TL;DR: In this article, the authors introduce the concept of the quotient space and the notion of automorphs for diophantine approximations of diophantas in the Euclidean space.
Book
Random matrices, Frobenius eigenvalues, and monodromy
Nicholas M. Katz,Peter Sarnak +1 more
TL;DR: In this paper, the main results of the main theorem were reformulated and reduction steps in proving the main theorems were taken in the following order: Test functions Haar measure Tail estimates Large $N$ limits and Fredholm determinants Several variables Equidistribution Monodromy of families of curves Monodromes of some other families GUE discrepancies in various families Distribution of low-lying Frobenius eigenvalues in different families Appendix AD: Densities Appendix AG: Graphs References.