Sums of Powers in Arithmetic Progressions
Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 505-506
Voir la notice de l'article provenant de la source Cambridge University Press
The papers [2] and [3] study the function g(k, n), defined for integers k > 1 and n > 1 as the smallest r with the property that every integer is a sum of r kth powers mod n. This note identifies g′(k), defined as the maximum over all n of g(k, n), with the function Γ(k) studied by Hardy and Littlewood [1] fifty years ago in connection with Waring's problem.
Small, Charles. Sums of Powers in Arithmetic Progressions. Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 505-506. doi: 10.4153/CMB-1978-087-7
@article{10_4153_CMB_1978_087_7,
author = {Small, Charles},
title = {Sums of {Powers} in {Arithmetic} {Progressions}},
journal = {Canadian mathematical bulletin},
pages = {505--506},
year = {1978},
volume = {21},
number = {4},
doi = {10.4153/CMB-1978-087-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-087-7/}
}
[1] 1. Hardy, G. H., Littlewood, J. E., and Pôlya, G., Inequalities. Cambridge University Press, New York, 1934. Google Scholar
[2] 2. Menon, K. V., An inequality for elementary symmetric functions. Canad. Math. Bull. vol. 15 (1), 1972, 133-135. Google Scholar
[3] 3. Whiteley, J. N., A generalization of a Theorem of Newton. Proc. American Math. Soc. 13 (1962), 144-151. Google Scholar
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