On Dirichlet series and Hecke triangle groups of infinite volume

Marvin I. Knopp; Mark Sheingorn

Acta Arithmetica (1996)

  • Volume: 76, Issue: 3, page 227-244
  • ISSN: 0065-1036

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Marvin I. Knopp, and Mark Sheingorn. "On Dirichlet series and Hecke triangle groups of infinite volume." Acta Arithmetica 76.3 (1996): 227-244. <http://eudml.org/doc/206897>.

@article{MarvinI1996,
author = {Marvin I. Knopp, Mark Sheingorn},
journal = {Acta Arithmetica},
keywords = {Dirichlet series of Riemann's functional equation; Mellin transforms; Riemann-Hecke-Bochner correspondence; modular integrals; Dirichlet series with functional equations; application of Eichler’s generalized Poincaré series; Hecke triangle group; finitely generated Fuchsian groups of the second kind},
language = {eng},
number = {3},
pages = {227-244},
title = {On Dirichlet series and Hecke triangle groups of infinite volume},
url = {http://eudml.org/doc/206897},
volume = {76},
year = {1996},
}

TY - JOUR
AU - Marvin I. Knopp
AU - Mark Sheingorn
TI - On Dirichlet series and Hecke triangle groups of infinite volume
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 3
SP - 227
EP - 244
LA - eng
KW - Dirichlet series of Riemann's functional equation; Mellin transforms; Riemann-Hecke-Bochner correspondence; modular integrals; Dirichlet series with functional equations; application of Eichler’s generalized Poincaré series; Hecke triangle group; finitely generated Fuchsian groups of the second kind
UR - http://eudml.org/doc/206897
ER -

References

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  1. [1] A. Beardon, The Geometry of Discrete Groups, Grad. Texts in Math. 91, Springer, New York, 1983. 
  2. [2] S. Bochner, Some properties of modular relations, Ann. of Math. 53 (1951), 332-363. Zbl0042.32101
  3. [3] K. Chandrasekharan and R. Narasimhan, Hecke's functional equation and arithmetical identities, Ann. of Math. 74 (1961), 1-23. Zbl0107.03702
  4. [4] M. Eichler, Grenzkreisgruppen und kettenbruchartige Algorithmen, Acta Arith. 11 (1965), 169-180. Zbl0148.32503
  5. [5] H. Hamburger, Über die Riemannsche Funktionalgleichung der ζ-Funktion, Math. Z. 10 (1921), 240-254. Zbl48.1210.03
  6. [6] E. Hecke, Herleitung des Euler-Produktes der Zetafunktion und einiger L-Reihen aus ihr Funktionalgleichung, Math. Ann. 119 (1944), 266-287. Zbl0028.40503
  7. [7] M. Knopp, A corona theorem for automorphic forms and related results, Amer. J. Math. 91 (1969), 599-618. Zbl0185.15402
  8. [8] M. Knopp, On Dirichlet series satisfying Riemann's functional equation, Invent. Math. 117 (1994), 361-372. Zbl0816.11032
  9. [9] M. Knopp, On the growth of entire automorphic integrals, Results in Math. 8 (1985), 146-152. Zbl0588.30051
  10. [10] M. Knopp, Some new results on the Eichler cohomology of automorphic forms, Bull. Amer. Math. Soc. 80 (1974), 607-632. Zbl0292.10022
  11. [11] J. Lehner, Automorphic forms with preassigned periods, J. Res. Nat. Bur. Standards Sect. B 73 (1969), 153-161. Zbl0185.33501
  12. [12] C. L. Siegel, Bemerkung zu einem Satz von Hamburger über die Funktionalgleichung der Riemannschen Zetafunktion, Math. Ann. 86 (1922), 276-279. Zbl48.1216.01

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