Open Access
Subscription Access
Open Access
Subscription Access
On Klingen Eisenstein Series with Level in Degree Two
Subscribe/Renew Journal
We give a representation theoretic approach to the Klingen lift in degree 2, generalizing the classical construction of Klingen Eisenstein series to arbitrary levels for both paramodular and Siegel congruence subgroups.
User
Subscription
Login to verify subscription
Font Size
Information
- Siegfried B¨ocherer, ¨Uber gewisse Siegelsche Modulformen zweiten Grades, Math. Ann., 261(1) (1982) 23–41.
- Siegfried B¨ocherer, ¨Uber die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen, Math. Z., 183(1) (1983) 21–46.
- Siegfried B¨ocherer and Rainer Schulze-Pillot, Siegel modular forms and theta series attached to quaternion algebras, Nagoya Math. J., 121 (1991) 35–96.
- Armand Brumer and Kenneth Kramer, Paramodular abelian varieties of odd conductor, Transactions of the American Mathematical Society, 366(5) (2014) 2463–2516.
- Martin Dickson, Hecke eigenvalues of Klingen–Eisenstein series of squarefree level, arXiv preprint arXiv:1512.09069 (2015).
- Wee Teck Gan and Shuichiro Takeda, The local Langlands conjecture for GSp(4), Ann. of Math. (2), 173(3) (2011) 1841–1882.
- Y. Kitaoka, A note on Klingen’s Eisenstein series, Abh. Math. Sem. Univ. Hamburg, 60 (1990) 95–114.
- Helmut Klingen, Zum Darstellungssatz f¨ur Siegelsche Modulformen, Math. Z., 102 (1967) 30–43.
- Helmut Klingen, Introductory lectures on Siegel modular forms, volume 20 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990).
- Nobushige Kurokawa and Shin-ichiro Mizumoto. On Eisenstein series of degree two, Proc. Japan Acad. Ser. A Math. Sci., 57(2) (1981) 134–139.
- Robert Langlands, On the notion of an automorphic representation. In Automorphic forms, representations and L-functions Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., (1977). Part 1, Proc. Sympos. Pure Math., XXXIII, pages 203–207. Amer. Math. Soc., Providence, R.I. (1979).
- Shin-ichiro Mizumoto, Fourier coeffients of generalized Eisenstein series of degree two, I. Invent. Math., 65(1) (1981/82) 115–135.
- Shin-ichiro Mizumoto, Fourier coefficients of generalized Eisenstein series of degree two, II. Kodai Math. J., 7(1) (1984) 86–110.
- Shin-ichiro Mizumoto, Nearly holomorphic Eisenstein liftings, Abh. Math. Sem. Univ. Hamburg, 67 (1997) 173–194.
- Goran Mui´c, Intertwining operators and composition series of generalized and degenerate principal series for Sp(4;R), Glas. Mat. Ser. III, 44(64)(2) (2009) 349–399.
- Cris Poor and David S. Yuen, The cusp structure of the paramodular groups for degree two, J. Korean Math. Soc., 50(2) (2013) 445–464.
- Cris Poor and David S. Yuen, Paramodular cusp forms, Math. Comp., 84(293) (2015) 1401–1438.
- Brooks Roberts, Global L-packets for GSp(2) and theta lifts, Doc. Math., 6 (2001) 247–314.
- Brooks Roberts and Ralf Schmidt, Local newforms for GSp(4), volume 1918 of Lecture Notes in Mathematics, Springer, Berlin, (2007).
- David Rohrlich, Elliptic curves and the Weil-Deligne group, In Elliptic curves and related topics, 4, (1994) 125–157.
- Ralf Schmidt, Archimedean aspects of Siegel modular forms of degree 2, Rocky Mountain J. Math., 47(7) (2017) 2381–2422.
- Ralf Schmidt, Packet structure and paramodular forms, Trans. Amer. Math. Soc., 370(5) (2018) 3085–3112.
- Alok Shukla, Codimensions of the spaces of cusp forms for Siegel congruence subgroups in degree two, Pacic J. Math., 293(1) (2018) 207–244.
Abstract Views: 575
PDF Views: 1