4 results
A Divisor Problem for Values of Polynomials
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- Journal:
- Canadian Mathematical Bulletin / Volume 35 / Issue 1 / 01 March 1992
- Published online by Cambridge University Press:
- 20 November 2018, pp. 108-115
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- 01 March 1992
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In this article we investigate the average order of the arithmetical function
where p1(t), p2(t) are polynomials in Z [t], of equal degree, positive and increasing for t ≥ 1. Using the modern method for the estimation of exponential sums ("Discrete Hardy-Littlewood Method"), we establish an asymptotic result which is as sharp as the best one known for the classical divisor problem.
Comportement Asymptotique de
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- Journal:
- Canadian Mathematical Bulletin / Volume 30 / Issue 3 / 01 September 1987
- Published online by Cambridge University Press:
- 20 November 2018, pp. 309-317
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- 01 September 1987
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Let {x} denote the fractional part of x. We find an asymptotic formula of
, where k is any positive integer and a is any real number ≥ 1, and so for the sum ∑n<xf(n), where f(n) belongs to a class of additive functions.
On a Result of Smith and Subbarao Concerning a Divisor Problem
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- Journal:
- Canadian Mathematical Bulletin / Volume 27 / Issue 4 / 01 December 1984
- Published online by Cambridge University Press:
- 20 November 2018, pp. 501-504
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- 01 December 1984
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Let d(n;l,k) denote the number of divisors of the positive integer n which are congruent to I modulo k. The objective of the present paper is to prove that (for some exponent θ<⅓)
holds uniformly in l, k and x satisfying 1≤l≤k≤x. This improves a recent result due to R. A. Smith and M. V. Subbarao [3].
Majorations Explicites Pour le Nombre de Diviseurs de N
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- Journal:
- Canadian Mathematical Bulletin / Volume 26 / Issue 4 / 01 December 1983
- Published online by Cambridge University Press:
- 20 November 2018, pp. 485-492
- Print publication:
- 01 December 1983
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Let
It is proved that the function f reaches its maximum for n = 6 983 776 800, and that maxn≥2f(n) = 1.5379. The proof deals with superior highly composite numbers introduced by Ramanujan.
