Abstract
It is well known that the Riemann zeta function, as well as several other L-functions, is universal in the strip \(1/2<\sigma <1\); this is certainly not true for \(\sigma >1\). Answering a question of Bombieri and Ghosh, we give a simple characterization of the analytic functions approximable by translates of L-functions in the half-plane of absolute convergence. Actually, this is a special case of a general rigidity theorem for translates of Dirichlet series in the half-plane of uniform convergence. Our results are closely related to Bohr’s equivalence theorem.
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Acknowledgements
This research was partially supported by PRIN-2015 Number Theory and Arithmetic Geometry. A.P. is member of the GNAMPA group of INdAM, and M.R. was partially supported by a research scholarship of the Department of Mathematics, University of Genova.
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Perelli, A., Righetti, M. A rigidity theorem for translates of uniformly convergent Dirichlet series. Arch. Math. 115, 647–656 (2020). https://doi.org/10.1007/s00013-020-01498-5
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DOI: https://doi.org/10.1007/s00013-020-01498-5