Dirichlet series and automorphic forms on unitary groups

Author:
Tobias Orloff

Journal:
Trans. Amer. Math. Soc. **290** (1985), 431-456

MSC:
Primary 11F55

DOI:
https://doi.org/10.1090/S0002-9947-1985-0792806-0

MathSciNet review:
792806

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In a special case our unitary group takes the form

**[1]**Armand Borel,*Reduction theory for arithmetic groups*, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 20–25. MR**0204533****[2]**Y. Flicker, -*packets and liftings for*, preprint.**[3]**Robert P. Langlands,*On the functional equations satisfied by Eisenstein series*, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin-New York, 1976. MR**0579181****[4]**O. T. O’Meara,*Introduction to quadratic forms*, Springer-Verlag, New York-Heidelberg, 1971. Second printing, corrected; Die Grundlehren der mathematischen Wissenschaften, Band 117. MR**0347768****[5]**Goro Shimura,*Arithmetic of unitary groups*, Ann. of Math. (2)**79**(1964), 369–409. MR**0158882**, https://doi.org/10.2307/1970551**[6]**Goro Shimura,*On modular forms of half integral weight*, Ann. of Math. (2)**97**(1973), 440–481. MR**0332663**, https://doi.org/10.2307/1970831**[7]**Goro Shimura,*The arithmetic of automorphic forms with respect to a unitary group*, Ann. of Math. (2)**107**(1978), no. 3, 569–605. MR**0563087**, https://doi.org/10.2307/1971129**[8]**Goro Shimura,*The special values of the zeta functions associated with Hilbert modular forms*, Duke Math. J.**45**(1978), no. 3, 637–679. MR**507462****[9]**Goro Shimura,*The arithmetic of certain zeta functions and automorphic forms on orthogonal groups*, Ann. of Math. (2)**111**(1980), no. 2, 313–375. MR**569074**, https://doi.org/10.2307/1971202**[10]**T. Shintani,*On automorphic forms on unitary groups of order*, preprint.**[11]**Stephen S. Kudla,*On certain Euler products for 𝑆𝑈(2,1)*, Compositio Math.**42**(1980/81), no. 3, 321–344. MR**607374****[12]**S. Gelbart and I. I. Piatetski-Shapiro,*Automorphic forms and*-*functions for the unitary group*, preprint 1983.**[13]**I. Piatetski-Shapiro,*Tate theory for reductive groups and distinguished representations*, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, pp. 585–590. MR**562659**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
11F55

Retrieve articles in all journals with MSC: 11F55

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0792806-0

Article copyright:
© Copyright 1985
American Mathematical Society