Bulletin of the Korean Mathematical Society (대한수학회보)

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CUSP FORMS IN S4 (Γ0 (79)) AND THE NUMBER OF REPRESENTATIONS OF POSITIVE INTEGERS BY SOME DIRECT SUM OF BINARY QUADRATIC FORMS WITH DISCRIMINANT -79

  • Kendirli, Baris (Department of Mathematics Faculty of Arts and Science Fatih University)
  • Received : 2011.01.07
  • Published : 2012.05.31
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Abstract

A basis of a subspace of $S_4({\Gamma}_0(79))$ is given and the formulas for the number of representations of positive integers by some direct sums of the quadratic forms $x^2_1+x_1x_2+20x^2_2$, $4x^2_1{\pm}x_1x_2+5x^2_2$, $2x^2_1{\pm}x_1x_2+10x^2_2$ are determined.

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References

  1. H. Ivaniec and E. Kowalski, Analytic Number Theory, American Mathematical Society Colloquium publications volume 53, 2000.
  2. G. Lomadze, On the number of representations of positive integers by a direct sum of binary quadratic forms with discriminant -23, Georgian Math. J. 4 (1997), no. 6, 523-532. https://doi.org/10.1023/A:1022103424996
  3. T. Miyake, Modular Forms, Springer-Verlag, 1989.

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