The number of ideals in a quadratic field |
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| Authors: | M. N. Huxley N. Watt |
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| Affiliation: | (1) School of Mathematics, University of Wales College of Cardiff, Senghenydd Road, CF2 4YH Cardiff, Wales, UK |
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| 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)|⩽Bk 50/73 N 23/73(logN)461/146 forN ≥Ak, whereA andB are constants. ForN ≥Ak c,C sufficiently large, the factork 50/73 may be replaced by (d(k))4/73 k 46/73. Dedicated to the memory of Professor K G Ramanathan |
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| Keywords: | Exponential sums character sums ideals quadratic field |
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