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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Computations of Siegel modular forms of genus two
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by Nils-Peter Skoruppa PDF
Math. Comp. 58 (1992), 381-398 Request permission

Abstract:

We explain the basic notions and theorems for doing computations in the theory of Siegel modular forms of degree two, on the full modular group and of even weight. This synopsis concludes with a handy and computationally realistic algorithm for tabulating the Fourier coefficients of such forms and the Euler factors of their Spinor zeta functions. In the second part of this paper we present and discuss some of the results of actual computations which we performed following this algorithm. We point out two (theoretically) striking phenomena that are implied by the results of these computations.
References
  • Anatolij N. Andrianov, Quadratic forms and Hecke operators, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 286, Springer-Verlag, Berlin, 1987. MR 884891, DOI 10.1007/978-3-642-70341-6
    • —, Euler products corresponding to Siegel modular forms of genus 2, Russian Math. Surveys 29 (1974), no. 3, 45-116. C. Batut, D. Bernardi, H. Cohen, and M. Olivier, PARI-GP, Université Bordeaux 1, Bordeaux, 1989.
  • Explicit methods in number theory, Oberwolfach Rep. 4 (2007), no. 3, 1957–2034. Abstracts from the workshop held July 15–21, 2007; Organized by Henri Cohen, Hendrik W. Lenstra and Don B. Zagier; Oberwolfach Reports. Vol. 4, no. 3. MR 2432111, DOI 10.4171/OWR/2007/34
  • Martin Eichler and Don Zagier, The theory of Jacobi forms, Progress in Mathematics, vol. 55, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 781735, DOI 10.1007/978-1-4684-9162-3
  • E. Freitag, Siegelsche Modulfunktionen, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 254, Springer-Verlag, Berlin, 1983 (German). MR 871067, DOI 10.1007/978-3-642-68649-8
  • Jun-ichi Igusa, On Siegel modular forms of genus two, Amer. J. Math. 84 (1962), 175–200. MR 141643, DOI 10.2307/2372812
  • Helmut Klingen, Zum Darstellungssatz für Siegelsche Modulformen, Math. Z. 102 (1967), 30–43 (German). MR 219473, DOI 10.1007/BF01110283
  • W. Kohnen and N.-P. Skoruppa, A certain Dirichlet series attached to Siegel modular forms of degree two, Invent. Math. 95 (1989), no. 3, 541–558. MR 979364, DOI 10.1007/BF01393889
  • Nobushige Kurokawa, Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two, Invent. Math. 49 (1978), no. 2, 149–165. MR 511188, DOI 10.1007/BF01403084
  • Hans Maass, Über eine Spezialschar von Modulformen zweiten Grades, Invent. Math. 52 (1979), no. 1, 95–104 (German). MR 532746, DOI 10.1007/BF01389857
  • Takayuki Oda, On the poles of Andrianov $L$-functions, Math. Ann. 256 (1981), no. 3, 323–340. MR 626953, DOI 10.1007/BF01679701
  • Nils-Peter Skoruppa, Über den Zusammenhang zwischen Jacobiformen und Modulformen halbganzen Gewichts, Bonner Mathematische Schriften [Bonn Mathematical Publications], vol. 159, Universität Bonn, Mathematisches Institut, Bonn, 1985 (German). Dissertation, Rheinische Friedrich-Wilhelms-Universität, Bonn, 1984. MR 806354
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 381-398
  • MSC: Primary 11F46; Secondary 11F60, 11F66
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1106982-0
  • MathSciNet review: 1106982