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A p-ADIC LIMIT OF SIEGEL–EISENSTEIN SERIES OF PRIME LEVEL q

YOSHINORI MIZUNO

Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany

https://doi.org/10.1142/S1793042108001729Cited by:2 (Source: Crossref)

Abstract

We show that a p-adic limit of a Siegel–Eisenstein series of prime level q becomes a Siegel modular form of level pq. This paper contains a simple formula for Fourier coefficients of a Siegel–Eisenstein series of degree two and prime levels.

Keywords:

AMSC: 11F33, 11F55

References

T. Arakawa, A note on Nagaoka's Eisenstein series from a view point of Saito Kurokawa lifting, unpublished preprint (1999) . Google Scholar
L. Carlitz, J. Reine. Angew. Math. 202, 174 (1959). Google Scholar
H. Cohen, Math. Ann. 217, 271 (1975), DOI: 10.1007/BF01436180. Crossref, Web of Science, Google Scholar
M. Eichler and D. Zagier, The Theory of Jacobi Forms 55 (Birkhauser Boston, Inc., Boston, MA, 1985) p. 148. Crossref, Google Scholar
E. Hecke, Math. Ann. 97, 210 (1926), DOI: 10.1007/BF01447866. Crossref, Google Scholar
F. Hirzebruch and D. Zagier, Invent. Math. 36, 57 (1976), DOI: 10.1007/BF01390005. Crossref, Web of Science, Google Scholar
G. Kaufhold, Math. Ann. 137, 454 (1959), DOI: 10.1007/BF01360845. Crossref, Web of Science, Google Scholar
H. Katsurada and S. Nagaoka, J. Number Theory 104(1), 100 (2004), DOI: 10.1016/S0022-314X(03)00160-4. Crossref, Web of Science, Google Scholar
H. Maass, Mat.-Fys. Medd. Danske Vid. Selsk. 38(14), 13 (1972). Google Scholar
T. Miyake, Modular Forms (Springer-Verlag, Berlin, 1989) p. 335. Crossref, Google Scholar
Y. Mizuno, An explicit arithmetic formula for Fourier coefficients of Siegel–Eisenstein series of degree two with square-free odd levels, preprint (2006) . Google Scholar
S. Nagaoka, Math. Z. 235, 227 (2000), DOI: 10.1007/s002090000134. Crossref, Web of Science, Google Scholar
J.-P. Serre, Formes Modulaires et Fonction Zeta p-Adiques, Lecture Notes in Math. 350 (Springer, Berlin, 1973) pp. 191–268. Crossref, Google Scholar
L. Washinton , Introduction to Cyclotomic Fields , General Texts in Mathematics 83 ( Springer-Verlag , 1997 ) . Crossref, Google Scholar
D. Zagier, Zetafunktionen und Quadratische Körper (Springer-Verlag, 1981) p. 144. Crossref, Google Scholar