Ω-theorems for the Riemann zeta-function
Norman Levinson (1972)
Acta Arithmetica
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Displaying similar documents to “On Karatsuba Conjecture and the Lindelöf Hypothesis”
Ω-theorems for the Riemann zeta-function
A limit theorem for the Riemann zeta-function in the complex space
A. Laurinčikas (1990)
Acta Arithmetica
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Three open problems and a conjecture
Huizeng Qin, Ovidiu Furdui (2015)
Open Mathematics
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In this paper we solve three open problems and a conjecture related to the calculations of some classes of multiple series posed by Furdui in [1].
More precise Pair Correlation Conjecture on the zeros of the Riemann zeta function
Tsz Ho Chan (2004)
Acta Arithmetica
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Note on a paper by H. L. Montgomery (Omega theorems for the Riemann zeta- function).
Ramachandra, K., Sankaranarayanan, A. (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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Borwein and Bradley's Apéry-like formulae for .
Almkvist, Gert, Granville, Andrew (1999)
Experimental Mathematics
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On Some Integrals Involving the Mean Square Formula for the Riemann Zeta-function
Aleksandar Ivić (1989)
Publications de l'Institut Mathématique
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On the Fourth Moment of the Riemann Zeta Functions
Aleksandar Ivić (1995)
Publications de l'Institut Mathématique
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On some conjectures and results for the Riemann zeta-function and Hecke series
Aleksandar Ivić (2001)
Acta Arithmetica
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A zero density result for the Riemann zeta function
Habiba Kadiri (2013)
Acta Arithmetica
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We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.
On large values of the Riemann zeta-function on short segments of the critical line
Maxim A. Korolev (2014)
Acta Arithmetica
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We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln{T}+c₀.