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3 results

  • AN AMAZING IDENTITY OF GAUSS AND JENKINS’ LEMMA

  • Part of
  • HENG HUAT CHAN, SONG HENG CHAN
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 108 / Issue 1 / August 2023
    Published online by Cambridge University Press:
    08 November 2022, pp. 86-98
    Print publication:
    August 2023
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  • We prove several finite product-sum identities involving the q-binomial coefficient, one of which is used to prove an amazing identity of Gauss. We then use this identity to evaluate certain quadratic Gauss sums and, together with known properties of quadratic Gauss sums, we prove the quadratic reciprocity law for the Jacobi symbol. We end our article with a new proof of Jenkins’ lemma, a lemma analogous to Gauss’ lemma. This article aims to show that Gauss’ amazing identity and the properties of quadratic Gauss sums are sufficient to establish the quadratic reciprocity law for the Jacobi symbol.

  • CODES ASSOCIATED WITH Sp(4,q) AND EVEN-POWER MOMENTS OF KLOOSTERMAN SUMS

  • Part of
  • JI HYUN KIM
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 79 / Issue 3 / June 2009
    Published online by Cambridge University Press:
    17 April 2009, pp. 427-435
    Print publication:
    June 2009
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  • Here we derive a recursive formula for even-power moments of Kloosterman sums or equivalently for power moments of two-dimensional Kloosterman sums. This is done by using the Pless power-moment identity and an explicit expression of the Gauss sum for Sp(4,q).

  • On a Product Related to the Cubic Gauss Sum, III

  • Hiroshi Ito
  • Journal:
    Canadian Journal of Mathematics / Volume 53 / Issue 2 / 01 April 2001
    Published online by Cambridge University Press:
    20 November 2018, pp. 310-324
    Print publication:
    01 April 2001
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  • We have seen, in the previous works [5], [6], that the argument of a certain product is closely connected to that of the cubic Gauss sum. Here the absolute value of the product will be investigated.