Geodesic
Quadratic polynomials, period polynomials, and Hecke operators
Marie Jameson1 ; Wissam Raji2
1 Department of Mathematics and Computer Science Emory University Atlanta, GA 30322, U.S.A.
2 Department of Mathematics American University of Beirut Beirut, Lebanon and fellow at Center for Advanced Mathematical Sciences Beirut, Lebanon
Acta Arithmetica, Tome 158 (2013) no. 3, pp. 287-297 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For any non-square $1 D\equiv 0,1$ (mod $4$), Zagier defined $$ F_{k}(D;x) :=\sum_{\substack {a,b,c \in \mathbb {Z},\, a 0\\ b^2-4ac=D }} \max(0,(ax^2+bx+c)^{k-1}). $$ Here we use the theory of periods to give identities and congruences which relate various values of $F_k(D;x).$
DOI : 10.4064/aa158-3-7
Keywords: non square equiv mod zagier defined sum substack mathbb max k here theory periods identities congruences which relate various values x

Marie Jameson 1 ; Wissam Raji 2

1 Department of Mathematics and Computer Science Emory University Atlanta, GA 30322, U.S.A.
2 Department of Mathematics American University of Beirut Beirut, Lebanon and fellow at Center for Advanced Mathematical Sciences Beirut, Lebanon 
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Marie Jameson; Wissam Raji. Quadratic polynomials, period polynomials,
 and Hecke operators. Acta Arithmetica, Tome 158 (2013) no. 3, pp. 287-297. doi: 10.4064/aa158-3-7

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