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On a conjecture of Duke-Imamoglu


Authors: Stefan Breulmann and Michael Kuß
Journal: Proc. Amer. Math. Soc. 128 (2000), 1595-1604
MSC (2000): Primary 11F46, 11F60, 11F30
DOI: https://doi.org/10.1090/S0002-9939-00-05586-6
Published electronically: February 7, 2000
MathSciNet review: 1707138
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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.


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  • [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: https://doi.org/10.1090/S0002-9939-00-05586-6
Received by editor(s): July 13, 1998
Published electronically: February 7, 2000
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2000 American Mathematical Society

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