Nonanalytic automorphic integrals on the Hecke groups

Paul C. Pasles

Acta Arithmetica (1999)

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

Abstract

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 In the present study, inspired by unpublished work of Knopp [Kn94], we consider the nonanalytic automorphic integral.

How to cite

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 In the present study, inspired by unpublished work of Knopp [Kn94], we consider the nonanalytic automorphic integral.},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