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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
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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
The Ramanujan journal, Vol.34(2), pp.187-208
06/2014
DOI: https://doi.org/10.1007/s11139-013-9480-4

Abstract

Article Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics and Statistics Combinatorics Mathematics Number Theory
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 F₁ = x₁² + x₁ x₂ + 6x₂² and Φ₁ = 2x₁² + x₁x₂ + 3x₂² (or its inverse) with discriminant −23.

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