On eisenstein series

Duke Mathematical Journal

Volumn 50, Issue 2, 1983, Pages 417-476

  Shimura, Goro ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972552022     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-83-05019-6     Document Type: Article

References (28)

1. J. ARTHUR, A trace formula for reductive groups I, Duke Math. J. 45 (1978), 911-952.
2. J. ARTHUR, Eisenstein series and the trace formula, Proc. Symp. Pure Math. 33 (1979), Part 1, 253-274.
3. E. BOREL, Sur une application d’un theoreme de M. Hadamard, Bull. Sei. Math. Ser. 2, 18 (1894), 22-25.
4. H. BRAUN, Zur Theorie der Hermitischen Formen, Abh. Math. Sem. Hamburg 14 (1941), 61-150.
5. W. CASSELMAN, A new non-unitary argument for p-adic representations, J. Fac. of Science, Univ. of Tokyo, Sec. IA, Math. 28 (1982), 907-928.
6. P. GARRETT, Arithmetic properties of Fourier-Jacobi expansions of automorphic forms in several variables, Amer. J. of Math. 103 (1981), 1103-1134.
7. J. GOLDMAN AND G.-C. ROTA, On the foundations of combinatorial theory IV, Studies in Appl. Math. 49 (1970), 239-258.
8. E. HECKE, Vorlesungen über die Theorie der algebraischen Zahlen, 1923, Chelsea, 1948.
9. E. HECKE, Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funk- tionentheorie und Arithmetik, Abh. Math. Sem. Hamburg 5 (1927), 199-224.
10. R. INDIK, Fourier coefficients of nonholomorphic Eisenstein series on a tube domain associated to an orthogonal group, Thesis, Princeton Univ. 1982.
11. G. KAUFHOLD, Dirichletsche Reihe mit Funktionalgleichung in der Theorie der Modulfunktion 2. Grades, Math. Ann. 137 (1959), 454-476.
12. H. D. KLOOSTERMAN, Theorie der Eisensteinschen Reihen von mehreren Veränderlichen, Abh. Math. Sem. Hamburg 6 (1928), 163-188.
13. K. F. LAI, Tamagawa number of reductive algebraic groups, Compositio Mathematica 41 (1980), 153-188.
14. R. P. LANGLANDS, Euler Products, Yale University Press, 1971.
15. R. P. LANGLANDS, On the functional equations satisfied by Eisenstein series, Lecture notes in Math. 544, Springer, 1976.
16. G. SHIMURA, Construction of class fields and zeta functions of algebraic curves, Ann. of Math. 85 (1967), 58-159.
17. G. SHIMURA, On some arithmetic properties of modular forms of one and several variables, Ann. of Math. 102 (1975), 491-515.
18. G. SHIMURA, On the Fourier coefficients of modular forms of several variables, Göttingen Nachr. Akad. Wiss. 1975, 261-268.
19. G. SHIMURA, The special values of the zeta functions associated with cusp forms, Comm. pure appl. Math. 29 (1976), 783-804.
20. G. SHIMURA, On the derivatives of theta functions and modular forms, Duke Math. J. 44 (1977), 365-387.
21. G. SHIMURA, The arithmetic of automorphic forms with respect to a unitary group, Ann. of Math. 107 (1978), 569-605.
22. G. SHIMURA, On certain reciprocity-laws for theta functions and modular forms, Acta Math. 141 (1978), 35-71.
23. G. SHIMURA, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. Ill (1980), 313-375.
24. G. SHIMURA, On certain zeta functions attached to two Hilbert modular forms: I, II, Ann. of Math. 114 (1981), 127-164, 569-607.
25. G. SHIMURA, Arithmetic of differential operators on symmetric domains, Duke Math. J. 48 (1981), 813-843.
26. G. SHIMURA, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), 269-302.
27. C. L. SIEGEL, Gesammelte Abhandlungen, I-IV, Springer.
28. J. STURM, The critical values of zeta functions associated to the symplectic group, Duke Math. J. 48 (1981), 327-350.