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.
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References
H. Davenport, On the distribution of quadratic residues (mod p), Journal of the London Mathematical Society 6 (1931), 49–54; 8 (1933), 46–52.
H. Davenport, On a principle of Lipschitz, Journal of the London Mathematical Society 26 (1951), 179–183.
P. Kurlberg and Z. Rudnick, The distribution of spacings between quadratic residues, submitted.
W. M. Schmidt, Northcott’s theorem on heights II. The quadratic case, Acta Arithmetica 70 (1995), 343–375.
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Supported in part by grants from the Israel Science Foundation and by the EC TMR network “Algebraic Lie Representations”, EC-contract no ERB FMRXCT97-010.
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Kurlberg, P. The distribution of spacings between quadratic residues, II. Isr. J. Math. 120, 205–224 (2000). https://doi.org/10.1007/s11856-000-1277-7
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DOI: https://doi.org/10.1007/s11856-000-1277-7