Geodesic
Nonanalytic automorphic integrals on the Hecke groups
Acta Arithmetica, Tome 90 (1999) no. 2, pp. 155-171.

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1. Introduction. Since its genesis over a century ago in work of Jacobi, Riemann, Poincar ́e and Klein [Ja29, Ri53, Le64], the theory of automorphic forms has burgeoned from a branch of analytic number theory into an industry all its own. Natural extensions of the theory are to integrals [Ei57, Kn94a, KS96, Sh94], thereby encompassing Hurwitz’s prototype, the analytic weight 2 Eisenstein series [Hu81], and to nonanalytic forms [He59, Ma64, Sel56, ER74, Fr85]. A generalization in both directions at once has also been the subject of some scrutiny. In the present study, inspired by unpublished work of Knopp [Kn94], we consider the nonanalytic automorphic integral.
DOI : 10.4064/aa-90-2-155-171
Keywords: automorphic integrals, modular integrals, weight-changing operators, Eisenstein series

Paul Pasles 1

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Paul Pasles. Nonanalytic automorphic integrals on the Hecke groups. Acta Arithmetica, Tome 90 (1999) no. 2, pp. 155-171. doi : 10.4064/aa-90-2-155-171. http://geodesic.mathdoc.fr/articles/10.4064/aa-90-2-155-171/

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