On the counting function of irregular primes
نویسنده
چکیده
It is well-known that there are infinitely many irregular primes. We prove a quantitative version of this statement, namely the number of such primes p ≤ x is at least (1 + o(1)) log log x/ log log log x as x → ∞. We show that the same conclusion holds for the irregular primes corresponding to the Euler numbers. Under some conditional results from diophantine approximation, the above lower bounds can be improved to log x/(log log x). 2010 Mathematics Subject Classification: Primary 11B68
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تاریخ انتشار 2014