Quadratic polynomials, period polynomials, and Hecke operators

Marie Jameson, and Wissam Raji. "Quadratic polynomials, period polynomials, and Hecke operators." Acta Arithmetica 158.3 (2013): 287-297. <http://eudml.org/doc/279134>.

@article{MarieJameson2013,
abstract = {For any non-square 1 < D ≡ 0,1 (mod 4), Zagier defined $F_\{k\}(D;x) :=∑_\{\begin\{array\}\{c\}a,b,c ∈ ℤ, a <0\\ b^2-4ac=D\end\{array\}\} max(0,(ax^2+bx+c)^\{k-1\})$. Here we use the theory of periods to give identities and congruences which relate various values of $F_k(D;x)$.},
author = {Marie Jameson, Wissam Raji},
journal = {Acta Arithmetica},
keywords = {period polynomials; quadratic polynomials},
language = {eng},
number = {3},
pages = {287-297},
title = {Quadratic polynomials, period polynomials, and Hecke operators},
url = {http://eudml.org/doc/279134},
volume = {158},
year = {2013},
}

TY - JOUR
AU - Marie Jameson
AU - Wissam Raji
TI - Quadratic polynomials, period polynomials, and Hecke operators
JO - Acta Arithmetica
PY - 2013
VL - 158
IS - 3
SP - 287
EP - 297
AB - For any non-square 1 < D ≡ 0,1 (mod 4), Zagier defined $F_{k}(D;x) :=∑_{\begin{array}{c}a,b,c ∈ ℤ, a <0\\ b^2-4ac=D\end{array}} max(0,(ax^2+bx+c)^{k-1})$. Here we use the theory of periods to give identities and congruences which relate various values of $F_k(D;x)$.
LA - eng
KW - period polynomials; quadratic polynomials
UR - http://eudml.org/doc/279134
ER -