• Transformation formula for exponential sums involving fourier coefficients of modular forms

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    • Keywords


      Exponential sums; summation formula; cusp forms and Maass forms; transformation formula

    • Abstract


      In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular groupSL(2, ℤ). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups ofSL(2, ℤ) and prove similar estimates for the corresponding Dirichlet series.

    • Author Affiliations


      C S Yogananda1

      1. Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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