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    • A simple method to extract zeros of certain Eisenstein series of small level

      ARADHITA CHATTOPADHYAYA

      Research Article Volume 130 Published: 10 January 2020 Article ID 0006

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/130/0006

    • Keywords

       

      Zeros of Eisenstein series; zeros of modular forms of $\Gamma_{0}(N)$.

    • Abstract

       

      This paper provides a simple method to extract the zeros of some weight two Eisenstein series of level $N$ where $N$ = 2, 3, 5 and 7. The method is based on the observation that these Eisenstein series are integral over the graded algebra of modular forms on $SL(2, Z)$ and their zeros are ‘controlled’ by those of $E_{4}$ and $E_{6}$ in the fundamental domain of $\Gamma_{0}(N)$.

    • Author Affiliations

       

      ARADHITA CHATTOPADHYAYA1

      1. Department of Centre for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India

    • Dates

       
      Published
      10 January 2020
      Manuscript received
      11 March 2019
      Manuscript revised
      15 June 2019
      Accepted
      22 June 2019
      Early published
      Unedited version published online
      Final version published online
      9 January 2020

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