Functiones et Approximatio Commentarii Mathematici

The number of representations of a positive integer by certain octonary quadratic forms

Şaban Alaca and Kenneth S. Williams

Full-text: Open access

Abstract

The number of representations of a positive integer by each of the octonary quadratic forms $x_1^2 +x_2^2 +3x_3^2 +3x_4^2 +3x_5^2 +3x_6^2 +3x_7^2 +3x_8^2$, $x_1^2 +x_2^2 +x_3^2 +x_4^2 +3x_5^2 +3x_6^2 +3x_7^2 +3x_8^2$, $x_1^2 +x_2^2 +x_3^2 +x_4^2 +x_5^2 +x_6^2 +3x_7^2 +3x_8^2$ is determined.

Article information

Source
Funct. Approx. Comment. Math., Volume 43, Number 1 (2010), 45-54.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.facm/1285679145

Digital Object Identifier
doi:10.7169/facm/1285679145

Mathematical Reviews number (MathSciNet)
MR2683573

Zentralblatt MATH identifier
1213.11087

Subjects
Primary: 11E25: Sums of squares and representations by other particular quadratic forms 11F27: Theta series; Weil representation; theta correspondences

Keywords
octonary quadratic forms representations theta functions Eisenstein series

Citation

Alaca, Şaban; Williams, Kenneth S. The number of representations of a positive integer by certain octonary quadratic forms. Funct. Approx. Comment. Math. 43 (2010), no. 1, 45--54. doi:10.7169/facm/1285679145. https://projecteuclid.org/euclid.facm/1285679145


Export citation

References

  • A. Alaca, \c S. Alaca and K. S. Williams, Evaluation of the convolution sums $\sum_l+12m =n \sigma (l) \sigma (m)$ and $\sum_3l+4m =n \sigma (l) \sigma (m)$, Adv. Theoretical Appl. Math. 1 (2006), 27--48.
  • A. Alaca, \c S. Alaca and K. S. Williams, The convolution sum $\sum_m < n/16 \sigma (m) \sigma (n-16m)$, Canad. Math. Bull. 51 (2008), 3--14.
  • A. Alaca, \c S. Alaca and K. S. Williams, Seven octonary quadratic forms, Acta Arith. 135 (2008), 339--350.
  • A. Alaca, \c S. Alaca and K. S. Williams, Fourteen octonary quadratic forms, Int. J. Number Theory 6 (2010), 37--50.
  • C. G. J. Jacobi, Fundamenta nova theoriae functionum ellipticarum, Bornträger, Regiomonti, 1829. (Gesammelte Werke, Erster Band, Chelsea Publishing Co., New York, 1969, pp. 49--239.)
  • G. Mason, On a system of elliptic modular forms attached to the large Mathieu group, Nagoya Math. J. 118 (1990), 177--193.
  • K. S. Williams, The convolution sum $\sum_m < n/8 \sigma(m) \sigma(n-8m)$, Pacific J. Math. 228 (2006), 387--396.