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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top- [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. Zbl0773.11031
- [Bo] A. Borel, Some finiteness properties of adele groups over number fields, Publ. Math. IHES 16 (1963), 5-30.
- [Ch] C. Chevalley, L'arithmétique dans les algèbres des matrices , Act. Sci. et Ind. 323, Hermann, Paris, 1936.
- [Co] H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217 (1975), 271-285. Zbl0311.10030
- [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.
- [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
- [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
- [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
- [Kr] A. Krieg, Eisenstein series on the four-dimensional hyperbolic space for Sp(1,ℍ), J. Number Theory 30 (1988), 177-198.
- [L] H. Leptin, Die Funktionalgleichung der Zeta-Funktion einer einfachen Algebra, Abh. Math. Sem. Hamburg 19 (1955), 198-221. Zbl0064.03704
- [Ma] H. Maass, Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen, Abh. Math. Sem. Hamburg 16 (1949), 72-100. Zbl0034.34801
- [Vi] M.-F. Vigneras, Arithmétique des algèbres de quaternions, Lecture Notes in Math. 800, Springer, Berlin, 1980. Zbl0422.12008
- [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.
- [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