2008/04/01 by Glyn Harman · 1 citation
Mathematics · #Analytic Number Theory Research #Mathematics and Applications #History and Theory of Mathematics
paper · doi:10.1142/s1793042108001316
openalex publication_date 2008/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/12
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 x ⅓ 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.