Eisenstein series on four-dimensional hyperbolic space

Valeri A. Gritsenko; Rainer Schulze-Pillot

Acta Arithmetica (1994)

  • Volume: 67, Issue: 3, page 241-268
  • ISSN: 0065-1036

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Valeri A. Gritsenko, and Rainer Schulze-Pillot. "Eisenstein series on four-dimensional hyperbolic space." Acta Arithmetica 67.3 (1994): 241-268. <http://eudml.org/doc/206630>.

@article{ValeriA1994,
author = {Valeri A. Gritsenko, Rainer Schulze-Pillot},
journal = {Acta Arithmetica},
keywords = {quaternion algebra; Eisenstein series; hyperbolic space; Fourier expansion; Cohen-Zagier -functions; meromorphic continuation; functional equation; Mellin transform; Dirichlet series; representation numbers; ternary quadratic forms; special values},
language = {eng},
number = {3},
pages = {241-268},
title = {Eisenstein series on four-dimensional hyperbolic space},
url = {http://eudml.org/doc/206630},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Valeri A. Gritsenko
AU - Rainer Schulze-Pillot
TI - Eisenstein series on four-dimensional hyperbolic space
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 3
SP - 241
EP - 268
LA - eng
KW - quaternion algebra; Eisenstein series; hyperbolic space; Fourier expansion; Cohen-Zagier -functions; meromorphic continuation; functional equation; Mellin transform; Dirichlet series; representation numbers; ternary quadratic forms; special values
UR - http://eudml.org/doc/206630
ER -

References

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  2. [Bo] A. Borel, Some finiteness properties of adele groups over number fields, Publ. Math. IHES 16 (1963), 5-30. 
  3. [Ch] C. Chevalley, L'arithmétique dans les algèbres des matrices , Act. Sci. et Ind. 323, Hermann, Paris, 1936. 
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  5. [E] M. Eichler, The basis problem for modular forms and the trace of the Hecke operators, in: Modular Functions of One Variable 1, Lecture Notes in Math. 320, Springer, Berlin, 1973, 75-151. 
  6. [EGM] J. Elstrodt, F. Grunewald, and J. Mennicke, Eisenstein series on three-dimensional hyperbolic space and imaginary quadratic number fields, J. Reine Angew. Math. 360 (1985), 160-213. Zbl0555.10012
  7. [Gr1] V. Gritsenko, Arithmetic of quaternions and Eisenstein series, Zap. Nauchn. Sem. LOMI 160 (1987), 82-90 (in Russian); English transl.: J. Soviet Math. 52 (1990), 3056-3062. Zbl0645.10027
  8. [Gr2] V. Gritsenko, Zeta-function of degree six of Hermitian modular forms of genus 2, Zap. Nauchn. Sem. LOMI 154 (1986), 46-66 (in Russian); English transl.: J. Soviet Math. 43 (1988), 2540-2553. Zbl0609.10022
  9. [Kr] A. Krieg, Eisenstein series on the four-dimensional hyperbolic space for Sp(1,ℍ), J. Number Theory 30 (1988), 177-198. 
  10. [L] H. Leptin, Die Funktionalgleichung der Zeta-Funktion einer einfachen Algebra, Abh. Math. Sem. Hamburg 19 (1955), 198-221. Zbl0064.03704
  11. [Ma] H. Maass, Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen, Abh. Math. Sem. Hamburg 16 (1949), 72-100. Zbl0034.34801
  12. [Vi] M.-F. Vigneras, Arithmétique des algèbres de quaternions, Lecture Notes in Math. 800, Springer, Berlin, 1980. Zbl0422.12008
  13. [Za1] D. B. Zagier, Modular forms whose Fourier coefficients involve zeta functions of quadratic fields, in: Modular Functions of One Variable 6, Lecture Notes in Math. 627, Springer, Berlin, 1977, 105-169. 
  14. [Za2] D. B. Zagier, The Rankin-Selberg method for automorphic functions which are not of rapid decay, J. Fac. Sci. Univ. Tokyo 28(1981), 415-437. Zbl0505.10011

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