• The number of ideals in a quadratic field

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      https://www.ias.ac.in/article/fulltext/pmsc/104/01/0157-0165

    • Keywords

       

      Exponential sums; character sums; ideals; quadratic field

    • Abstract

       

      LetK be a quadratic Geld, and letR(N) be the number of integer ideals inK with norm at most AT. Letx with conductork be the quadratic character associated withK. Then |R(N)−NL(1,x)|⩽Bk50/73N23/73(logN)461/146 forNAk, whereA andB are constants. ForNAkc,C sufficiently large, the factork50/73 may be replaced by (d(k))4/73k46/73.

    • Author Affiliations

       

      M N Huxley1 N Watt1

      1. School of Mathematics, University of Wales College of Cardiff, Senghenydd Road, Cardiff, Wales - CF2 4YH, UK
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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