Hostname: page-component-74656f9884-c52kr Total loading time: 0 Render date: 2026-11-09T04:58:14.601Z Has data issue: false hasContentIssue false
  • English
  • Français

Partial Gaussian sums III

Published online by Cambridge University Press:  18 May 2009

D. A. Burgess
D. A. Burgess
Affiliation:
Department of Mathematics, University of Nottingham, Nottingham NG7 2RD
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

For integers a, N and H > 0 write

where ϰ denotes a non-principal Dirichlet character modulo the positive integer k and e(y) denotes e2πiy. By a well-known generalisation of the Póya–Vinogradov inequality

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 253 - 261
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Burgess, D. A., ‘On character sums and L-series II’, Proc London Math Soc (3) 13 (1963) 524–536.CrossRefGoogle Scholar
2.Burgess, D. A., ‘Estimation of character sums modulo a power of a prime’, Proc London Math Soc (3) 52 (1986) 215–235.CrossRefGoogle Scholar
3.Burgess, D. A., ‘The character sum estimate with r = 3 J London Math Soc (2) 33 (1986) 219–226.CrossRefGoogle Scholar
4.Burgess, D. A., ‘Partial Gaussian sums’, Bull London Math Soc 20 (1988) 589–592.CrossRefGoogle Scholar
5.Burgess, D. A., ‘Partial Gaussian sums II’, Bull London Math Soc 21 (1989), 153–158.CrossRefGoogle Scholar
6.Burgess, D. A., ‘On a set of congruences related to character sums III’, to be published in J. London Math. Soc.Google Scholar
7.Schmidt, W. M., Equations over finite fields. An elementary approach, Lecture Notes in Mathematics 536 (Springer Verlag 1976).CrossRefGoogle Scholar
8.Vinogradov, A. I., ‘On the symmetry property of sums with Dirichlet characters’ (Russian), Izv Akad Nauk UzSSR Ser Fiz-Mat Nauk 9 (1965) 21–27.Google Scholar