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CUSP FORMS IN S40 (79)) AND THE NUMBER OF REPRESENTATIONS OF POSITIVE INTEGERS BY SOME DIRECT SUM OF BINARY QUADRATIC FORMS WITH DISCRIMINANT -79

  • Kendirli, Baris
  • Received : 2011.01.07
  • Published : 2012.05.31

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.

Keywords

cusp forms;representation number;theta series

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.

Cited by

  1. Representations by Certain Sextenary Quadratic Forms Whose Coefficients Are 1, 2, 3 and 6 vol.06, pp.04, 2016, https://doi.org/10.4236/apm.2016.64018
  2. The Bases of and the Number of Representation of Integers vol.2013, 2013, https://doi.org/10.1155/2013/695265
  3. Fourier Coefficients of a Class of Eta Quotients of Weight 16 with Level 12 vol.06, pp.08, 2015, https://doi.org/10.4236/am.2015.68133
  4. Cusp forms in S 6(Γ 0(23)), S 8(Γ 0(23)) and the number of representations of numbers by some quadratic forms in 12 and 16 variables vol.34, pp.2, 2014, https://doi.org/10.1007/s11139-013-9480-4