Estimates for character sums
HTML articles powered by AMS MathViewer
- by J. Friedlander and H. Iwaniec PDF
- Proc. Amer. Math. Soc. 119 (1993), 365-372 Request permission
Abstract:
We give a number of estimates for character sums \[ \sum \limits _{a \in \mathcal {A}} {\sum \limits _{b \in \mathcal {B}} {\chi (a + b)} } \] for rather general sets $\mathcal {A},\;\mathcal {B}$. These give, in particular, a modified proof of the inequalities of Pólya-Vinogradov and of Burgess, which displays the latter as a generalization of the former.References
- D. A. Burgess, On character sums and primitive roots, Proc. London Math. Soc. (3) 12 (1962), 179–192. MR 132732, DOI 10.1112/plms/s3-12.1.179
- D. A. Burgess, On character sums and $L$-series. II, Proc. London Math. Soc. (3) 13 (1963), 524–536. MR 148626, DOI 10.1112/plms/s3-13.1.524
- Edward Dobrowolski and Kenneth S. Williams, An upper bound for the sum $\sum ^{a+H}_{n=a+1}f(n)$ for a certain class of functions $f$, Proc. Amer. Math. Soc. 114 (1992), no. 1, 29–35. MR 1068118, DOI 10.1090/S0002-9939-1992-1068118-6
- John Friedlander, Primes in arithmetic progressions and related topics, Analytic number theory and Diophantine problems (Stillwater, OK, 1984) Progr. Math., vol. 70, Birkhäuser Boston, Boston, MA, 1987, pp. 125–134. MR 1018373
- John B. Friedlander and Henryk Iwaniec, Incomplete Kloosterman sums and a divisor problem, Ann. of Math. (2) 121 (1985), no. 2, 319–350. With an appendix by Bryan J. Birch and Enrico Bombieri. MR 786351, DOI 10.2307/1971175
- Adolf Hildebrand, Large values of character sums, J. Number Theory 29 (1988), no. 3, 271–296. MR 955953, DOI 10.1016/0022-314X(88)90106-0 G. Pólya, Über die Verteilung der quadratischen Reste und Nichtreste, Königl. Ges. Wiss. Göttingen Nachr. (1918), 21-29. I. M. Vinogradov, On the distribution of power residues and non-residues, J. Phys. Math. Soc. Perm Univ. 1 (1918), 94-98; Selected works, Springer, Berlin, 1985, pp. 53-56.
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 365-372
- MSC: Primary 11L40
- DOI: https://doi.org/10.1090/S0002-9939-1993-1152276-X
- MathSciNet review: 1152276