# Nonanalytic automorphic integrals on the Hecke groups

Acta Arithmetica (1999)

- Volume: 90, Issue: 2, page 155-171
- ISSN: 0065-1036

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topPaul C. Pasles. "Nonanalytic automorphic integrals on the Hecke groups." Acta Arithmetica 90.2 (1999): 155-171. <http://eudml.org/doc/207320>.

@article{PaulC1999,

abstract = {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 In the present study, inspired by unpublished work of Knopp [Kn94], we consider the nonanalytic automorphic integral.},

author = {Paul C. Pasles},

journal = {Acta Arithmetica},

keywords = {automorphic integrals; modular integrals; weight-changing operators; Eisenstein series; nonanalytic automorphic integral; log-polynomial sum; weight-changing operator; Hecke group},

language = {eng},

number = {2},

pages = {155-171},

title = {Nonanalytic automorphic integrals on the Hecke groups},

url = {http://eudml.org/doc/207320},

volume = {90},

year = {1999},

}

TY - JOUR

AU - Paul C. Pasles

TI - Nonanalytic automorphic integrals on the Hecke groups

JO - Acta Arithmetica

PY - 1999

VL - 90

IS - 2

SP - 155

EP - 171

AB - 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 In the present study, inspired by unpublished work of Knopp [Kn94], we consider the nonanalytic automorphic integral.

LA - eng

KW - automorphic integrals; modular integrals; weight-changing operators; Eisenstein series; nonanalytic automorphic integral; log-polynomial sum; weight-changing operator; Hecke group

UR - http://eudml.org/doc/207320

ER -

## References

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