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On a hybrid bound for twisted L-values

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Abstract

Let f ∈S k (M, ψ) be a newform, and let χ be a primitive character of conductor q. We express \({L(\frac{1}{2}+it,f\otimes\chi)}\) as a short combination of bilinear forms involving Kloosterman fractions. Using this we establish the convexity breaking bound \({L\left(\tfrac{1}{2}+it,f\otimes\chi\right)\ll_{f,\varepsilon} [q(1+|t|)]^{\frac{1}{2}-\frac{1}{118}+\varepsilon}}\) for any ε > 0.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai, 400005, India

    Ritabrata Munshi

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  1. Ritabrata Munshi
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Correspondence to Ritabrata Munshi.

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A part of this work was done while the author was a member at the Institute for Advanced Study, Princeton. The author wishes to thank the Institute for providing a stimulating atmosphere conducive to intensive research. During the stay the author was supported by an NSF grant through the Institute. The author also thanks the referee for many valuable suggestions.

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Munshi, R. On a hybrid bound for twisted L-values. Arch. Math. 96, 235–245 (2011). https://doi.org/10.1007/s00013-011-0227-4

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  • DOI: https://doi.org/10.1007/s00013-011-0227-4

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