Application of limit theorem to sum of Legendre symbols. (English) Zbl 1424.11143
Summary: In this work, we make an extension of earlier results provided by J. P. Kubilius and Yu. V. Linnik [Izv. Vyssh. Uchebn. Zaved., Mat. 1959, No. 6(13), 88–95 (1959; Zbl 0104.03802)] who modelled specific class of Brownian motions using the sums of H. Davenport and P. Erdős [Publ. Math. 2, 252–265 (1953; Zbl 0050.04302)]. Our results are relevant and can be used in a range of applications, especially when applying Monte-Carlo methods in finance and econometrics.
MSC:
| 11N64 | Other results on the distribution of values or the characterization of arithmetic functions |
| 11L07 | Estimates on exponential sums |
| 11N60 | Distribution functions associated with additive and positive multiplicative functions |
| 60F05 | Central limit and other weak theorems |
