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Estimates for L-functions in the Critical Strip Under GRH with Effective Applications
被引：3
|作者：
Simonic, Aleksander
[1
]
机构：
[1] Univ New South Wales Canberra, Sch Sci, Canberra, ACT, Australia
关键词：
Selberg class;
Riemann hypothesis;
Mertens function;
explicit results;
EXPLICIT UPPER;
BOUNDS;
D O I：
10.1007/s00009-023-02289-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Assuming the generalized Riemann hypothesis, we provide explicit upper bounds for moduli of logL(s) and L'(s)/L(s) in the neighbourhood of the 1-line when L(s) are the Riemann, Dirichlet and Dedekind zeta-functions. To do this, we generalize Littlewood's wellknown conditional result to functions in the Selberg class with a polynomial Euler product, for which we also establish a suitable convexity estimate. As an application, we provide conditional and effective estimates for the Mertens function.
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页数：24
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