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Quadratic congruences on average and rational points on cubic surfaces

Volume 171 / 2015

Stephan Baier, Ulrich Derenthal Acta Arithmetica 171 (2015), 145-171 MSC: Primary 11D45; Secondary 14G05, 11G35. DOI: 10.4064/aa171-2-3

Abstract

We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is ${\mathbf A}_5+{\mathbf A}_1$.

Authors

  • Stephan BaierTata Institute of Fundamental Research
    1 Dr. Homi Bhabha Road
    Colaba, Mumbai 400005, India
    e-mail
  • Ulrich DerenthalInstitut f\"ur Algebra, Zahlentheorie und Diskrete Mathematik
    Leibniz Universit\"at Hannover
    Welfengarten 1
    30167 Hannover, Germany
    e-mail

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