Abstract
Luo has proven an optimal upper bound for the \(L^4\)-norm of dihedral Maass forms of large eigenvalue, by bounding a mean value of triple product L-functions. Motivated by this result, we study a mean value of L-functions having similar shape, and obtain for it an asymptotic with power savings. Our work may be helpful in eventually obtaining an asymptotic for the \(L^4\)-norm.
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Acknowledgments
We are grateful to Valentin Blomer and Matthew Young for very helpful discussions regarding this project. The first author was supported by a Grant from the European Research Council (Grant Agreement Number 258713) when he was based at the University of Göttingen and thanks Texas A&M University at Qatar, where part of this work was done, for its hospitality.
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Buttcane, J., Khan, R. A mean value of a triple product of L-functions. Math. Z. 285, 565–591 (2017). https://doi.org/10.1007/s00209-016-1721-y
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DOI: https://doi.org/10.1007/s00209-016-1721-y