Residue properties of certain quadratic units |
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Authors: | Kenneth Kramer |
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Institution: | Department of Mathematics, Queens College (CUNY), Flushing, New York 11367 USA |
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Abstract: | Explicit formulas are given for the quadratic and quartic characters of units of certain quadratic fields in terms of representations by positive definite binary quadratic forms, as conjectured by Leonard and Williams (Pacific J. Math.71 (1977), Rocky Mountain J. Math.9 (1979)), and by Lehmer (J. Reine Angew. Math.268/69 (1974)). For example, if p and a are primes such that p≡1 (mod 8), q≡5 (mod 8) and the Legendre symbol , and if ε is the fundamental unit of (√q), then , where p=a2+16b2 and pk=c2+16qd2 with k odd. |
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