A new lower bound for (3/2)k - Wadim Zudilin
A new lower bound for (3/2)k - Wadim Zudilin
A new lower bound for (3/2)k - Wadim Zudilin
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A <strong>new</strong> <strong>lower</strong> <strong>bound</strong> <strong>for</strong> ‖(3/2) k ‖ 9In addition, from (13)–(15) and the prime number theorem we deduce that(21)log Φ(αm, βm, γm)C 2 = limm→∞ mC 2 ′ log Φ ′ (αm, βm, γm)= limm→∞ m==∫ 10∫ 10ϕ(x) dψ(x),ϕ ′ (x) dψ(x),where ψ(x) is the logarithmic derivative of the gamma function and the1-periodic functions ϕ(x) and ϕ ′ (x) are defined as follows:ϕ(x) = min ̂ϕ(x, y),0≤y