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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 1

On the Dedekind sums and the quadratic Gauss sums

Wang TINGTING
Zhang WENPENG
Sayfa
77–83
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, we use the analytic method and properties of the Gauss sums to study one kind of mean value computational problem involving the Dedekind sums and the quadratic Gauss sums, and give an exact computational formula and asymptotic formula for it.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we use the analytic method and properties of the Gauss sums to study one kind of mean value computational problem involving the Dedekind sums and the quadratic Gauss sums, and give an exact computational formula and asymptotic formula for it.
📊
Temel Bulgular & Veri:In this paper, we use the analytic method and properties of the Gauss sums to study one kind of mean value computational problem involving the Dedekind sums and the quadratic Gauss sums, and give an exact computational formula and asymptotic formula for it.
💡
Sonuç & Katkı:In this paper, we use the analytic method and properties of the Gauss sums to study one kind of mean value computational problem involving the Dedekind sums and the quadratic Gauss sums, and give an exact computational formula and asymptotic formula for it.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we use the analytic method and properties of the Gauss sums to study one kind of mean value computational problem involving the Dedekind sums and the quadratic Gauss sums, and give an exact computational formula and asymptotic formula for it.

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Bu Makaleye Atıf Yap

TINGTING, W., WENPENG, Z. (2022). On the Dedekind sums and the quadratic Gauss sums. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 1, 77–83. https://ajindex.com/articles/530485

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Kaynakça (9)

  1. Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory (Springer-Verlag, New York, 1976)
  2. Carlitz, L. The reciprocity theorem of Dedekind sums, Pacific J. Math. 3, 513-522, 1953
  3. Chaohua, J. On the mean value of Dedekind sums, Journal of Number Theory 87, 173-188, 2001
  4. Conrey, J. B., Fransen, E., Klein, R. and Scott, C. Mean values of Dedekind sums, Journal of Number Theory 56, 214-226, 1996
  5. Rademacher, H. Dedekind Sums (Carus Mathematical Monographs, Math. Assoc. Amer., Washington D.C., 1972)
  6. Rademacher, H. On the transformation of log ?7(t), J. Indian Math. Soc. 19, 25-30, 1955
  7. Wenpeng, Z. A note on the mean square value of the Dedekind sums, Acta Mathematica Hungarica 86, 275-289, 2000
  8. Wenpeng, Z., Yuan, Y. and Xiali, H. On the 2k-th power mean of Dirichlet L-functions with the weight of general Kloosterman sums, Journal of Number Theory 84, 199-213, 2000
  9. Wenpeng, Z. On the mean values of Dedekind sums, Journal de Theorie des Nombres de Bordeaux 8, 429-442, 1996.