The Inconsistency Problem of Riemann Zeta Function Equation
نویسندگان
چکیده
منابع مشابه
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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) and we set T 0 E * (t) dt = 3πT /4 + R(T), then we obtain R(T) = O ε (T 593/912+ε), T 0 R 4 (t) dt ≪ ε T 3+ε , and T 0 R 2 (t) dt = T 2 P 3 (log T) + O ε (T 11/6+ε), whe...
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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 ∫ T 0 |E(t)| dt ≪ε T 2+ε and ∫ T 0 |E∗(t)| 544 75 dt ≪ε T 601 225 . It is also shown how bounds for moments of |E∗(t)| lead to bounds for moments of |ζ( 1 2 ...
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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 ∫ T 0 (E(t)) dt ≪ε T . We also show how our method of proof yields the bound R
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ژورنال
عنوان ژورنال: Mathematics Letters
سال: 2019
ISSN: 2575-503X
DOI: 10.11648/j.ml.20190502.11