Distribution of squares modulo a composite number

Preprint English OPEN
Aryan, Farzad;
  • Subject: Mathematics - Number Theory
    arxiv: Mathematics::Number Theory

In this paper we study the distribution of squares modulo a square-free number $q$. We also look at inverse questions for the large sieve in the distribution aspect and we make improvements on existing results on the distribution of $s$-tuples of reduced residues.
  • References (21)
    21 references, page 1 of 3

    [1] F. Aryan, The distribution of k-tuples of reduced residues, Mathematika. (2014). http://dx.doi.org/10.1112/S0025579314000151.

    [2] F. Aryan, Incomplete Kloosterman sum, Math Overflow question (2014), http://mathoverflow.net/questions/175822/incomplete-kloosterman-sum

    [3] D. Burgess, The distribution of quadratic residues and non-residues. Mathematika, 4. (1957).

    [4] H. Cramer, On the order of magnitude of the difference between consecutive prime numbers. Acta Arithmetica.(1936).

    [5] H. Davenport, Multiplicative number theory, Springer Verlag, (2000).

    [6] H. Davenport, On the distribution of quadratic residues (mod p). J. London Math. Soc. (1931).

    [7] P. Erdős, The difference of consecutive primes. Duke Math. (1940).

    [8] B. Green, On a variant of the large sieve, preprint available at arXiv:0807.5037. (2008).

    [9] B. Green and A. Harper, Inverse questions for the large sieve. To appear in GAFA.

    [10] A. Granville, P. Kurlberg, Poisson statistics via the Chinese remainder theorem. Adv. Math. (2008).

  • Metrics
Share - Bookmark