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Creators/Authors contains: "Bui, Hung M"

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  1. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract Assuming the Riemann Hypothesis, we study negative moments of the Riemann zeta-function and obtain asymptotic formulas in certain ranges of the shift in ζ ⁢ ( s ) {\zeta(s)}. For example, integrating | ζ ⁢ ( 1 2 + α + i ⁢ t ) | - 2 ⁢ k {|\zeta(\frac{1}{2}+\alpha+it)|^{-2k}}with respect totfromTto 2 ⁢ T {2T}, we obtain an asymptotic formula when the shift α is roughly bigger than 1 log ⁡ T {\frac{1}{\log T}}and k < 1 2 {k<\frac{1}{2}}. We also obtain non-trivial upper bounds for much smaller shifts, as long as log ⁡ 1 α ≪ log ⁡ log ⁡ T {\log\frac{1}{\alpha}\ll\log\log T}. This provides partial progress towards a conjecture of Gonek on negative moments of the Riemann zeta-function, and settles the conjecture in certain ranges. As an application, we also obtain an upper bound for the average of the generalized Möbius function. 
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  2. ; ; ; (, Acta Arithmetica)
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  3. ; ; (, Journal of Number Theory)
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  4. ; ; ; (, Algebra & Number Theory)
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