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- W2000281359 abstract "Since [x/p] = [[x]/p], it is clear that (3) then holds for all real x>0. We propose to show in this note that the order of ir(x) =the number of primes less than or equal x (a result originally due to Tschebyschef, cf. [1 ]) may be derived very quickly from (3) as a consequence of a general theorem which has no particular relationship to prime numbers. This is of some further interest in that Landau, in [i, p. 82], says effectively that (3) does not suffice to give Tschebyschef's theorem. Our general theorem, which is in the nature of a weak Tauberian theorem, is as follows. THEOREM. Let an,> 0 be a sequence of real numbers such that" @default.
- W2000281359 created "2016-06-24" @default.
- W2000281359 creator A5043687819 @default.
- W2000281359 date "1950-03-01" @default.
- W2000281359 modified "2023-09-26" @default.
- W2000281359 title "On the number of primes less than or equal $x$" @default.
- W2000281359 cites W1515528048 @default.
- W2000281359 doi "https://doi.org/10.1090/s0002-9939-1950-0036260-7" @default.
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