Zobrazeno 1 - 10 of 16 pro vyhledávání: '"Karl K Norton"'
2
On the frequencies of large values of divisor functions
Autor: Karl K. Norton
Publikováno v: Acta Arithmetica. 68:219-244
where ζ is the Riemann zeta-function and s > 1. It follows from (1.2) that for any positive integer k, dk(n) is the number of ordered k-tuples (n1, . . . , nk) of positive integers such that n1 . . . nk = n. In particular, d2(n) is the number of dis
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::770784aa2b8644e8575d01eb492f01fd
https://doi.org/10.4064/aa-68-3-219-244
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3
On the number of restricted prime factors of an integer. II
Autor: Karl K. Norton
Publikováno v: Acta Math. 143 (1979), 9-38
We usually write co(n; P)=co(n), ~2(n; P ) = ~ ( n ) . In a previous paper [37], we obtained sharp inequalities for the frequencies of large deviations of co(n; E) and ~(n; E) from their normal order of magnitude. Those inequalities included refineme
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::353c4499d84a47ca120c840cc3c8292b
https://doi.org/10.1007/bf02392087
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4
Estimates for partial sums of the exponential series
Autor: Karl K Norton
Publikováno v: Journal of Mathematical Analysis and Applications. 63(1):265-296
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6
On character sums and power residues
Autor: Karl K. Norton
Publikováno v: Transactions of the American Mathematical Society. 167:203-226
Sharp estimates are given for a double sum involving Dirichlet characters. These are applied to the problem of estimating certain sums whose values give a measure of the average distance between successive power residues to an arbitrary modulus. A pa
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fabe79ac13aaeb75dc0db7cd6d58096c
https://doi.org/10.1090/s0002-9947-1972-0296034-8
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9
Upper bounds for sums of powers of divisor functions
Autor: Karl K. Norton
Publikováno v: Journal of Number Theory. (1):60-85
Let ζ be the Riemann zeta-function and write ζ(s)2 = Σn >- 1 dz(n)n−s for real s > 1, z > 1, so that dz(n) is a generalized divisor function. We obtain good upper bounds for Dz(x, t) = Σn ≤ x(dz(n))t which are uniform in the real variables x,
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