The Distribution of Spacings between Quadratic Residues
نویسنده
چکیده
We study the distribution of spacings between squares modulo q, where q is square-free and highly composite, in the limit as the number of prime factors of q goes to infinity. We show that all correlation functions are Poissonian, which among other things, implies that the spacings between nearest neighbors, normalized to have unit mean, have an exponential distribution. Date: Dec 14, 1998. Supported in part by a grant from the Israel Science Foundation. In addition, the first author was partially supported by the EC TMR network ”Algebraic Lie Representations”, EC-contract no ERB FMRX-CT97-0100. 1
منابع مشابه
The Distribution of Spacings between Quadratic Residues, Ii
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.
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