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Journal of Mathematical Sciences

, Volume 89, Issue 2, pp 1079–1081 | Cite as

Computation of the number representations of the elements of the ringℤ/dℤ as a sum of squares

  • G. V. Abramov
  • P. M. Vinnik
Article
  • 14 Downloads

Abstract

The number of representations of the elements of the ringℤ/dℤ as a sum of invertible squares is computed, provided that each square occurs in the sum no more tha a fized number of times. For prime d an exhaustive answer is given in term of the class number and the fundamental unit of the real quadratic field\(\mathbb{Q}(\sqrt d )\). Biblography: 5 titles.

Keywords

Number Representation Class Number Fundamental Unit Quadratic Field Real Quadratic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Z. I. Borevich and I. R. Shfarevich,Number Theory [in Russian], Moscow (1985).Google Scholar
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    N. C. Ankeny, E. Artin, and S. Chowla, “The class number of real quadratic field”,Ann. Math. 56, 479–493 (1952).MathSciNetGoogle Scholar
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    L. J. Mordell, “On a Pellian equation conjecture”,Acta Arith.,6, 137–144 (1960).MATHMathSciNetGoogle Scholar
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    N. C. Ankeny and S. Chowla, “A further note on the class number, of real quadratic fields,”Acta Arith.,7, No. 3, 271–272 (1962).MathSciNetGoogle Scholar
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    A. A. Kiselev, “An expression of the ideal class number of real quadratic fields in terms of Bernoulli numbers”,Dokl. Akad. Nauk SSSR,61, 777–779 (1948).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • G. V. Abramov
  • P. M. Vinnik

There are no affiliations available

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