On Solving a Curious Inequality of Ramanujan
نویسندگان
چکیده
Ramanujan proved that the inequality π(x) < ex log x π (x e ) holds for all sufficiently large values of x. Using an explicit estimate for the error in the prime number theorem, we show unconditionally that it holds if x ≥ exp(9658). Furthermore, we solve the inequality completely on the Riemann Hypothesis, and show that x = 38, 358, 837, 682 is the largest integer counterexample.
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ورودعنوان ژورنال:
- Experimental Mathematics
دوره 24 شماره
صفحات -
تاریخ انتشار 2015