Quadratic polynomials, period polynomials, and Hecke operators

Marie Jameson; Wissam Raji

Acta Arithmetica, Tome 161 (2013), p. 287-297 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $F_{k} (D; x)$ .

Publié le : 2013-01-01

Zbl 1280.11027

EUDML-ID : urn:eudml:doc:279134

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-7,
     author = {Marie Jameson and Wissam Raji},
     title = {Quadratic polynomials, period polynomials, and Hecke operators},
     journal = {Acta Arithmetica},
     volume = {161},
     year = {2013},
     pages = {287-297},
     zbl = {1280.11027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-7}
}

Marie Jameson; Wissam Raji. Quadratic polynomials, period polynomials, and Hecke operators. Acta Arithmetica, Tome 161 (2013) pp. 287-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-7/