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On a conjecture of Duke-Imamoglu

Author(s): Stefan Breulmann; Michael Kuß
Journal: Proc. Amer. Math. Soc. 128 (2000), 1595-1604.
MSC (2000): Primary 11F46, 11F60, 11F30
Posted: February 7, 2000
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Abstract:

In this note we present some theoretical results and numerical calculations on a recent conjecture of W. Duke and Ö. Imamoglu.

References:

[An1]
A.N. Andrianov, Euler products corresponding to Siegel modular forms of genus 2, Russ. Math. Surveys 29, No. 3 (1974), 45-116. MR 55:5540

[An2]
A.N. Andrianov, Quadratic Forms and Hecke Operators, Springer-Verlag, Berlin, Heidelberg, New York, 1987. MR 88g:11028
[Bö]
S. Böcherer, Siegel modular forms and theta series, Proc. Symp. Pure Math. 49, Pt. 2 (1989), 3-17. MR 90i:11049

[BFW]
R.E. Borcherds, E. Freitag, R. Weissauer, A Siegel cusp form of degree 12 and weight 12, J. Reine Angew. Math. 494 (1998), 141-153. MR 99d:11047

[De]
P. Deligne, La conjecture de Weil, Publ. Math. I.H.E.S. 43 (1973), 273-307. MR 49:5013

[DI]
W. Duke, Ö. Imamoglu, Siegel modular forms of small weight, Math. Ann. 310 (1998), 73-82. MR 98m:11037

[EZ]
M. Eichler, D. Zagier, The Theory of Jacobi Forms, Birkhäuser, Boston, Basel, Stuttgart, 1985. MR 86j:11043

[Fr]
E. Freitag, Siegelsche Modulfunktionen, Springer-Verlag, Berlin, Heidelberg, New York, 1983. MR 88b:11027

[Kr]
A. Krieg, Das Vertauschungsgesetz zwischen Hecke- Operatoren und dem Siegelschen $\Phi$-Operator, Arch. Math. 46 (1986), 323-329. MR 87i:11064

[Le]
D.H. Lehmer, Ramanujan's function $\tau(n)$, Duke Math. J. 10 (1943), 483-492. MR 5:35b

[Ma]
H. Maaß, Die Primzahlen in der Theorie der Siegelschen Modulfunktionen, Math. Ann. 124 (1951), 87-122. MR 13:823g

[Mi]
I. Miyawaki, Numerical examples of Siegel cusp forms of degree 3 and their zeta-functions, Mem. Fac. Sci., Kyushu Univ., Ser. A 46, No. 2 (1992), 307-339. MR 94e:11049

[Si]
C.L. Siegel, Über die analytische Theorie der quadratischen Formen, Ann. of Math. (2) 36 (1935), 527-606.

[We]
R. Weissauer, Stabile Modulformen und Eisensteinreihen, Lecture Notes in Mathematics 1219, Springer-Verlag, Berlin, Heidelberg, New York, 1986. MR 89g:11041

[Za]
N.A. Zarkovskaja, The Siegel operator and Hecke operators, Funct. Anal. Appl. 8 (1974), 113-120. MR 50:2082

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Additional Information:

Stefan Breulmann
Affiliation: Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: stefan.breulmann@urz.uni-heidelberg.de

Michael Kuß
Affiliation: Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: michael.kuss@urz.uni-heidelberg.de

DOI: 10.1090/S0002-9939-00-05586-6
PII: S 0002-9939(00)05586-6
Received by editor(s): July 13, 1998
Posted: February 7, 2000
Communicated by: Dennis A. Hejhal
Copyright of article: Copyright 2000, American Mathematical Society

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