Geodesic
On Functional Properties of Incomplete Gaussian Sums
Canadian journal of mathematics, Tome 43 (1991) no. 1, pp. 182-212

Voir la notice de l'article provenant de la source Cambridge University Press

The following special function of two real variables x2 and x1 is considered: and its connections with the incomplete Gaussian sums where ω are intervals of length |ω| ≤1. In particular, it is proved that for each fixed x2 and uniformly in X2 the function H(x2, x1 ) is of weakly bounded 2-variation in the variable x1 over the period [0, 1]. In terms of the sums W this means that for collections Ω = {ωk}, consisting of nonoverlapping intervals ωk ∪ [0,1) the following estimate is valid: where card denotes the number of elements, and c is an absolute positive constant. The exact value of the best absolute constant к in the estimate (which is due to G. H. Hardy and J. E. Littlewood) is discussed. 
Oskolkov, K. I. On Functional Properties of Incomplete Gaussian Sums. Canadian journal of mathematics, Tome 43 (1991) no. 1, pp. 182-212. doi: 10.4153/CJM-1991-010-0
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