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- W4292265074 abstract "Let ζ be the zeta function. In this paper, we prove that the function ϕ ( x , y ) defined on ( 1 , ∞ ) 2 by ϕ ( x , y ) = 2 − x ζ ( x ) − 2 − y ζ ( y ) ζ ( x ) − ζ ( y ) if x ≠ y and ϕ ( x , x ) = ( 1 − ζ ( x ) ζ ′ ( x ) ln 2 ) 1 2 x , is strictly increasing in both x and y on ( 1 , ∞ ) . This gives a positive answer to a guess and an open problem. As applications, we obtain some new functional inequalities involving the ζ -function, and find a pair of simple but accurate lower and upper bounds for the ζ -function at odd integers." @default.
- W4292265074 created "2022-08-19" @default.
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- W4292265074 date "2023-01-01" @default.
- W4292265074 modified "2023-09-24" @default.
- W4292265074 title "Monotonicity results involving the zeta function with applications" @default.
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- W4292265074 doi "https://doi.org/10.1016/j.jmaa.2022.126609" @default.
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