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The Ramanujan Journal

, Volume 34, Issue 2, pp 187–208 | Cite as

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

  • Bülent Köklüce
Article

Abstract

In this study we find bases of S 6(Γ 0(23)), S 8(Γ 0(23)) and obtain explicit formulae for the number of representations of numbers by some quadratic forms in 12 and 16 variables that are direct sums of binary quadratic forms \(F_{1}=x_{1}^{2}+x_{1}x_{2}+6x_{2}^{2}\) and \(\varPhi_{1}=2x_{1}^{2}+x_{1}x_{2}+3x_{2}^{2}\) (or its inverse) with discriminant −23.

Keywords

Quadratic forms Representation numbers Theta series Cusp forms 

Mathematics Subject Classification (2010)

11E25 11E76 

Notes

Acknowledgements

The author would like to thank the anonymous referee for the careful reading and nice comments. The author would also like to thank Prof. Barış Kendirli for his helpful comments.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsFatih UniversityIstanbulTurkey

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