Geodesic
Quadratic polynomials, period polynomials, and Hecke operators
Marie Jameson1 ; Wissam Raji2
1Department of Mathematics and Computer Science Emory University Atlanta, GA 30322, U.S.A.
2Department 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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