Lower Bounds for Least Quadratic Non-Residues

  • S. W. Graham
  • C. J. Ringrose
Part of the Progress in Mathematics book series (PM, volume 85)


Let p be a prime, and let n p denote the least positive integer n such that n is a quadratic non-residue mod p. In 1949, Fridlender [F] and Salié [Sa] independently showed that \( {n_p} = \Omega \left( {\log p} \right) \); in other words, there are infinitely many primes p such that \( {n_p} \geqslant c\log p \) for some absolute constant c. In 1971, Montgomery showed that if the Generalized Riemann Hypothesis is true, then
$$ {n_p} = \Omega \left( {\log p\log \log p} \right) $$


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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • S. W. Graham
    • 1
  • C. J. Ringrose
    • 2
  1. 1.Department of MathematicsMichigan Technological UniversityHoughtonUSA
  2. 2.LeedsEngland

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