On the holomorphy of certain dirichlet series

Proceedings of the London Mathematical Society

Volumn s3-31, Issue 1, 1975, Pages 79-98

  Shimura, Goro ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84959748775     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1112/plms/s3-31.1.79     Document Type: Article

References (12)

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2. H. Jacquet and R. P. Langlands Automorphic forms on GL(2), Part II, Lecture notes in mathematics 278 (Springer, Berlin, 1972).
3. H. Maass, ‘Konstruktion ganzer Modulformen halbzahliger Dimension mit -Multiplikatoren in einer und zwei Variablen’, Abh. Math. Sem. Univ. Hamburg 12 (1937) 133-62.
4. A. P. Ogg, ‘On a convolution of L-series’, Invent. Math. 7 (1969) 297-312.
5. H. Petersson, ‘Über die systematische Bedeutung der Eisensteinschen Reihen’, Abh. Math. Sem. Univ. Hamburg 16 (1949) 104-30.
6. R. A. Rankin, ‘Contributions to the theory of Ramanujan’s function r(n) and similar arithmetical functions, I, II’, Proc. Cambridge Philos. Soc. 35 (1939) 351-72.
7. G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11 (Iwanami Shoten and Princeton University Press, 1971).
8. G. Shimura, ‘On modular forms of half integral weight’, Ann. of Math. 97 (1973) 440-81.
9. G. Shimura, ‘Modular forms of half integral weight’, Proc. Int. Summer School on modular functions (Antwerp, 1972); Lecture notes in mathematics 320 (Springer, Berlin, 1973), pp. 57-74.
10. C. L. Siegel, Lectures on advanced analytic number theory (Tata Institute of Fundamental Research, Bombay, 1961).
11. C. L. Siegel, ‘Die Funktionalgleichungen einiger Dirichletscher Reihen’, Math. Z. 63 (1956) 363-73 (= Abh. Ill, 228-38).
12. C. L. Siegel, ‘A generalization of the Epstein zeta function’, J. Indian Math. Soc. 20 (1956) 1-10 (= Abh. Ill, 239-48).