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Bounds for Fourier-Jacobi Coefficients of Siegel Cusp Forms of Degree Two

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L-Functions and Automorphic Forms

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 10))

Abstract

We discuss and prove several estimates involving Peterrson norms of Fourier-Jacobi coefficients of Siegel cusp forms of degree two.

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References

  1. Andrianov, A.N.: Euler products corresponding to Siegel modular forms of genus 2. Math. Surv. 29, 45–116 (1974)

    Article  MATH  Google Scholar 

  2. Böcherer, S., Raghavan, S.: On Fourier coefficients of Siegel modular forms. J. Reine Angew. Math. 384, 80–101 (1988)

    MathSciNet  MATH  Google Scholar 

  3. Breulmann, S.: On Hecke eigenforms in the Maaß space. Math. Z. 232, 527–530 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eichler, M., Zagier, D.: The Theory of Jacobi Forms. Progress in Mathematics, vol. 55. Birkhäuser, Boston (1985)

    Google Scholar 

  5. Gun, S., Sengupta, J.: Sign changes of Fourier coefficients of Siegel cusp forms of degree two on Hecke congruence subgroups. Int. J. Number Theory 13(10), 2597–2625 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Iwaniec, H.: Topics in Classical Automorphic Forms. Graduate Studies in Mathematics, vol. 17. American Mathematical Society, Providence, RI (1997)

    Google Scholar 

  7. Kohnen, W.: Estimates for Fourier coefficients of Siegel cusp forms of degree two. Compos. Math. 87, 231–240 (1993)

    MathSciNet  MATH  Google Scholar 

  8. Kohnen, W.: On a conjecture of Resnikoff and Saldaña. Bull. Aust. Math. Soc. 56, 235–237 (1997)

    Article  MATH  Google Scholar 

  9. Kohnen, W.: On the growth of the Petersson norms of Fourier-Jacobi coefficients of Siegel cusp forms. Bull. Lond. Math. Soc. 43, 717–720 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kohnen, W., Skoruppa, N.-P.: A certain Dirichlet series attached to Siegel modular forms of degree two. Invent. Math. 95, 541–558 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  11. Resnikoff, H.L., Saldaña, R.L.: Some properties of Fourier coefficients of Eisenstein series of degree two. J. Reine Angew. Math. 265, 90–109 (1974)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Heidelberg, INF 205, 69120, Heidelberg, Germany

    Winfried Kohnen

  2. School of Mathematics, T.I.F.R., Homi Bhabha Road, Mumbai, 400 005, India

    Jyoti Sengupta

Authors
  1. Winfried Kohnen
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  2. Jyoti Sengupta
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Corresponding author

Correspondence to Jyoti Sengupta .

Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Jan Hendrik Bruinier

  2. Mathematisches Institut, Universität Heidelberg, Heidelberg, Germany

    Winfried Kohnen

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Kohnen, W., Sengupta, J. (2017). Bounds for Fourier-Jacobi Coefficients of Siegel Cusp Forms of Degree Two. In: Bruinier, J., Kohnen, W. (eds) L-Functions and Automorphic Forms. Contributions in Mathematical and Computational Sciences, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-69712-3_9

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