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11-XX Number theory
11Fxx Discontinuous groups and automorphic forms
11F33 Congruences for modular and $p$ -adic modular forms

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Quadratic polynomials, period polynomials, and Hecke operators

Marie Jameson, Wissam Raji (2013)

Acta Arithmetica

For any non-square 1 < D ≡ 0,1 (mod 4), Zagier defined $F_{k} (D; x) : = \sum_{\begin{matrix} a, b, c \in ℤ, a < 0 \\ b^{2} - 4 a c = D \end{matrix}} m a x (0, {(a x^{2} + b x + c)}^{k - 1})$ . Here we use the theory of periods to give identities and congruences which relate various values of $F_{k} (D; x)$ .

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