Quartic Residues and Binary Quadratic Forms

@inproceedings{Sun2005QuarticRA,
  title={Quartic Residues and Binary Quadratic Forms},
  author={Zhi-Hong Sun},
  year={2005}
}
Let p ≡ 1 (mod 4) be a prime, m ∈ Z and p m. In this paper we obtain a general criterion for m to be a quartic residue (mod p) in terms of appropriate binary quadratic forms. Let d > 1 be a squarefree integer such that ( d p ) = 1, where ( d p ) is the Legendre symbol, and let εd be the fundamental unit of the quadratic field Q( √ d). Since 1942 many mathematicians tried to characterize those primes p so that εd is a quadratic or quartic residue (mod p). In this paper we will completely solve… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 18 references

Supplements to the theory of quartic residues

  • Z. H. Sun
  • Acta Arith
  • 2001

Gauss and Jacobi Sums

  • B. C. Berndt, R. J. Evans, K. S. Williams
  • John Wiley & Sons, Inc., New York, Chichester
  • 1998

A Course in Computational Algebraic Number Theory

  • H. Cohen
  • Graduate Texts in Mathematics 138, Springer…
  • 1993

Primes of the Form x2 + ny2: Fermat

  • D. A. Cox
  • Class Field Theory, and Complex Multiplication…
  • 1989

On the quartic residue of quadratic units of negative

  • Y. Chuman, N. Ishii
  • norm, Math. Japonica
  • 1987

Konstruktion von Klassenkorpern und Potenzrestkriterien fur quadratische Einheiten

  • F. Halter-Koch
  • Manuscripta Math
  • 1986

Ring class fields modulo 8 of Q ( √ − m ) and the quartic character of units of Q ( √ m ) for m ≡ 1 mod 8

  • N. Ishii
  • Osaka J . Math .
  • 1986

A Classical Introduction to Modern Number Theory

  • K. Ireland, M. Rosen
  • Springer, New York
  • 1982

On quadratic and quartic characters of quadratic units, Sci

  • Y. Furuta, P. Kaplan
  • Rep. Kanazawa Univ
  • 1981

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