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Estimates for character sums


Authors: J. Friedlander and H. Iwaniec
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
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Abstract: We give a number of estimates for character sums

$\displaystyle \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 [Enhancements On Off] (What's this?)

  • [B1] D. A. Burgess, On character sums and primitive roots, Proc. London Math. Soc. (3) 12 (1962), 179-192. MR 0132732 (24:A2569)
  • [B2] -, On character sums and $ L$-series. II, Proc. London Math. Soc. (3) 13 (1963), 524-536. MR 0148626 (26:6133)
  • [DW] E. Dobrowolski and K. S. Williams, An upper bound for the sum $ \sum\nolimits_{n = a + 1}^{a + H} {f(n)} $ for a certain class of functions $ f$, Proc. Amer. Math. Soc. 114 (1992), 29-35. MR 1068118 (92c:11086)
  • [F] J. Friedlander, Primes in arithmetic progressions and related topics, Analytic Number Theory and Diophantine Problems (Proc. Conf. Oklahoma State Univ. 1984) (Adolphson, Conrey, Ghosh, and Yager, eds.), Birkhäuser, Boston, PM, 70, 1987, pp. 125-134. MR 1018373 (90h:11086)
  • [FI] J. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem, Ann. of Math. (2) 121 (1985), 319-350. MR 786351 (86i:11050)
  • [H] A. Hildebrand, Large values of character sums, J. Number Theory 29 (1988), 271-296. MR 955953 (89k:11073)
  • [P] G. Pólya, Über die Verteilung der quadratischen Reste und Nichtreste, Königl. Ges. Wiss. Göttingen Nachr. (1918), 21-29.
  • [V] 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.

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DOI: https://doi.org/10.1090/S0002-9939-1993-1152276-X
Article copyright: © Copyright 1993 American Mathematical Society

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