Abstract
In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire L-functions in the critical strip, under the generalized Riemann hypothesis. The examples include the entire Dirichlet L-functions \(L(s,\chi )\) for primitive characters \(\chi \).
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Notes
Throughout the paper we use the notation \(f \ll g\) to mean that for a certain constant \(C>0\) we have \(f(t) \le Cg(t)\) for \(t\in Dom(f) \cap Dom(g)\). In the subscript we indicate the parameters in which such constant C may depend on.
Throughout the paper we use the notation \(f = O(g)\) to mean that for a certain constant \(C>0\) we have \(|f(t)|\le Cg(t)\) for t sufficiently large. In the subscript we indicate the parameters in which such constant C may depend on.
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Acknowledgements
The author thanks Emanuel Carneiro and Vorrapan Chandee for inspiring discussions. The author acknowledges support from FAPERJ—Brazil.
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Chirre, A. A Note on Entire L-Functions. Bull Braz Math Soc, New Series 50, 67–93 (2019). https://doi.org/10.1007/s00574-018-0092-x
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DOI: https://doi.org/10.1007/s00574-018-0092-x