On the mean square value of the Hurwitz zeta-function
نویسندگان
چکیده
منابع مشابه
On the distribution of zeros of the Hurwitz zeta-function
Assuming the Riemann hypothesis, we prove asymptotics for the sum of values of the Hurwitz zeta-function ζ(s, α) taken at the nontrivial zeros of the Riemann zeta-function ζ(s) = ζ(s, 1) when the parameter α either tends to 1/2 and 1, respectively, or is fixed; the case α = 1/2 is of special interest since ζ(s, 1/2) = (2s − 1)ζ(s). If α is fixed, we improve an older result of Fujii. Besides, we...
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Let ∆(x) denote the error term in the Dirichlet divisor problem, and E(T ) the error term in the asymptotic formula for the mean square of |ζ( 1 2 + it)|. If E∗(t) = E(t) − 2π∆∗(t/2π) with ∆∗(x) = −∆(x) + 2∆(2x) − 1 2 ∆(4x), then we obtain the asymptotic formula ∫ T 0 (E(t)) dt = T P3(logT ) +Oε(T ), where P3 is a polynomial of degree three in log T with positive leading coefficient. The expone...
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Let ∆(T ) and E(T ) be the error terms in the classical Dirichlet divisor problem and in the asymptotic formula for the mean square of the Riemann zeta function in the critical strip, respectively. We show that ∆(T ) and E(T ) are asymptotic integral transforms of each other. We then use this integral representation of ∆(T ) to give a new proof of a result of M. Jutila.
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1994
ISSN: 0019-2082
DOI: 10.1215/ijm/1255986887