Euler's 0-function and Its Iterates
نویسنده
چکیده
Remarks . In the case r = 1 the simple lower bound Vj (x) > x(x) is available . When r = 2, the analogous result is V2(x) > 7c 2 (x) where 7r 2 (x) denotes the number of primes p < x such that (p 1)/2 is prime . Evidently the numbers 02(p) = (p -3)/2 are distinct . Sieve theory suggests, but of course does not yet prove, that 7r 2(x) > x/log 2 x, so that apart from the second factor on the right our estimate is probably sharp . We hope to return to the lower bound problem : our best result so far is x/log' x for some fixed k > 2 . It may be that for every fixed r and every e > 0 we have x/(log x)r + E < V'(x) < x/(Iog x),E
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