Transformation formula for exponential sums involving fourier coefficients of modular forms
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In 1984 Jutila  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, . 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.
Volume 133, 2023
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