论文信息 - WATT'S MEAN VALUE THEOREM AND CARMICHAEL NUMBERS

WATT'S MEAN VALUE THEOREM AND CARMICHAEL NUMBERS

It is shown that Watt's new mean value theorem on sums of character sums can be included in the method described in the author's recent work [6] to show that the number of Carmichael numbers up to x exceeds x⅓ for all large x. This is done by comparing the application of Watt's original version of his mean value theorem [8] to the problem of primes in short intervals [3] with the problem of finding "small" primes in an arithmetic progression.

Glyn Harman

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[5] Glyn Harman. On the Number of Carmichael Numbers up to x , 2005 .

[6] J. Chernick. On Fermat's simple theorem , 1939 .

[7] Elias M. Stein,et al. Models of degenerate Fourier integral operators and Radon transforms , 1994 .