Eisenstein series on four-dimensional hyperbolic space
Valeri A. Gritsenko ; Rainer Schulze-Pillot
Acta Arithmetica, Tome 68 (1994), p. 241-268 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:206630 
@article{bwmeta1.element.bwnjournal-article-aav67i3p241bwm,
     author = {Valeri A. Gritsenko and Rainer Schulze-Pillot},
     title = {Eisenstein series on four-dimensional hyperbolic space},
     journal = {Acta Arithmetica},
     volume = {68},
     year = {1994},
     pages = {241-268},
     zbl = {0810.11035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav67i3p241bwm}
}

Valeri A. Gritsenko; Rainer Schulze-Pillot. Eisenstein series on four-dimensional hyperbolic space. Acta Arithmetica, Tome 68 (1994) pp. 241-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav67i3p241bwm/

[000] [BS] S. Böcherer and R. Schulze-Pillot, The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2, Math. Z. 209 (1992), 273-287. | Zbl 0773.11031

[001] [Bo] A. Borel, Some finiteness properties of adele groups over number fields, Publ. Math. IHES 16 (1963), 5-30.

[002] [Ch] C. Chevalley, L'arithmétique dans les algèbres des matrices , Act. Sci. et Ind. 323, Hermann, Paris, 1936.

[003] [Co] H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217 (1975), 271-285. | Zbl 0311.10030

[004] [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.

[005] [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. | Zbl 0555.10012

[006] [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. | Zbl 0645.10027

[007] [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. | Zbl 0609.10022

[008] [Kr] A. Krieg, Eisenstein series on the four-dimensional hyperbolic space for Sp(1,ℍ), J. Number Theory 30 (1988), 177-198.

[009] [L] H. Leptin, Die Funktionalgleichung der Zeta-Funktion einer einfachen Algebra, Abh. Math. Sem. Hamburg 19 (1955), 198-221. | Zbl 0064.03704

[010] [Ma] H. Maass, Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen, Abh. Math. Sem. Hamburg 16 (1949), 72-100. | Zbl 0034.34801

[011] [Vi] M.-F. Vigneras, Arithmétique des algèbres de quaternions, Lecture Notes in Math. 800, Springer, Berlin, 1980. | Zbl 0422.12008

[012] [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.

[013] [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. | Zbl 0505.10011