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Number Theory pp 153-162 | Cite as

Jac obsthal sums in terms of quadratic partitions of a prime

  • S. A. Katre
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1122)

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References

  1. [1]
    B.C. Berndt and R.J. Evans, Sums of Gauss, Jacobi, and Jacobsthal, J. Number Th. 11 (1979), 349–398.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J.W.S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press (1967), p.284.Google Scholar
  3. [3]
    H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklichen Fallen, J. reine angen. Math. 172 (1935), 151–182.MathSciNetzbMATHGoogle Scholar
  4. [4]
    S.A. Katre and A.R. Rajwade, On the Jacobsthal sum ø4(a) and the related sum ψ8(a), to appear in Math. Student.Google Scholar
  5. [5]
    S.A. Katre and A.R. Rajwade, On the Jacobsthal sum ø9(a) and the related sum ψ9(a), Math. Scand. 53 (1983).Google Scholar
  6. [6]
    E. Lehmer, On the number of solutions of uk + D = w2 (mod p), Pacific J. Math. 5 (1955), 103–118.MathSciNetCrossRefGoogle Scholar
  7. [7]
    E. Lehmer, On Euler's criterion, J. Austral.Math.Soc.1(1959), 64–70.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    P.A. Leonard and K.S. Williams, Evaluation of certain Jacobsthal sums, Boll. Un. Mat. Ital. B(5) 15 (1978), 717–723.MathSciNetzbMATHGoogle Scholar
  9. [9]
    A.R. Rajwade, On rational primes p congruent to 1 (mod 3 or 5), Proc. Camb. Phil. Soc. 66 (1969), 61–70.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    A.L. Whiteman, Cyclotomy and Jacobsthal's sums, Amer. J. Math., 74 (1952), 89–99.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    K.S. Williams, Note on a cubic character sum, Aequ. Math. 12 (1975), 229–231.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    K.S. Williams, On Euler's Criterion for quintic nonresidues, Pac. J. Math. 61 (1975), 543–550.CrossRefzbMATHGoogle Scholar

Additional references

  1. [13]
    R.J. Evans, Determinations of Jacobsthal sums, Pacific J. Math. (to appear).Google Scholar
  2. [14]
    R.H. Hudson and K.S. Williams, Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums, Pacific J.Math. 99 (1982), 379–386.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [15]
    R.H. Hudson and K.S. Williams, An application of Western's formulae to the evaluation of certain Jacobsthal sums, Acta Arith. 41 (1982), 261–276.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • S. A. Katre
    • 1
  1. 1.Centre for Advanced Study in MathematicsPanjab UniversityChandigarhIndia

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