Abstract
A recent method of Soundararajan enables one to obtain improved Ω-result for finite series of the form ∑ n f(n) cos (2πλ n x+β) where 0≤λ1≤λ2≤. . . and β are real numbers and the coefficients f(n) are all non-negative. In this paper, Soundararajan’s method is adapted to obtain improved Ω-result for E(t), the remainder term in the mean-square formula for the Riemann zeta-function on the critical line. The Atkinson series for E(t) is of the above type, but with an oscillating factor (−1)n attached to each of its terms.
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Lau, YK., Tsang, KM. Omega result for the mean square of the Riemann zeta function. manuscripta math. 117, 373–381 (2005). https://doi.org/10.1007/s00229-005-0565-2
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DOI: https://doi.org/10.1007/s00229-005-0565-2