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Estimates on the zeros of \(E_2\)

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Abstract

We improve the results from El Basraoui (Proc Amer Math Soc 138(7):2289–2299, 2010) about the Eisenstein series \(E_2(z)=1-24\sum _{n=1}^\infty \frac{nq^n}{1-q^n}\). In particular we show that there exists exactly one (simple) zero in each Ford circle and give an approximation to its location.

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Acknowledgments

We thank the referees for numerous and extremely helpful comments and corrections on an earlier version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, ETH, Zurich, Switzerland

    Özlem Imamoḡlu & Jonas Jermann

  2. Eotvos Lorand University, Budapest, Hungary

    Árpád Tóth

Authors
  1. Özlem Imamoḡlu
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  2. Jonas Jermann
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  3. Árpád Tóth
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Corresponding author

Correspondence to Özlem Imamoḡlu.

Additional information

Communicated by Jens Funke.

Ö. Imamoglu and J. Jermann are supported by SNF 200020-144285, Á. Tóth is supported by OTKA grants NK 104183 and NK81203.

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Imamoḡlu, Ö., Jermann, J. & Tóth, Á. Estimates on the zeros of \(E_2\) . Abh. Math. Semin. Univ. Hambg. 84, 123–138 (2014). https://doi.org/10.1007/s12188-014-0091-9

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  • DOI: https://doi.org/10.1007/s12188-014-0091-9

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