Geodesic
Large character sums
Granville, Andrew1 ; Soundararajan, K.2, 3
1 Department of Mathematics, University of Georgia, Athens, Georgia 30602
2 Department of Mathematics, Princeton University, Princeton, New Jersey 08544
3 School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Journal of the American Mathematical Society, Tome 14 (2001) no. 2, pp. 365-397

Voir la notice de l'article provenant de la source American Mathematical Society

We make conjectures and give estimates for how large character sums can be as we vary over all characters mod $q$, and as we vary over real, quadratic characters. In particular we show that the largest sums seem to depend on the value of the character at “smooth numbers”.
DOI : 10.1090/S0894-0347-00-00357-X

Granville, Andrew 1 ; Soundararajan, K. 2, 3

1 Department of Mathematics, University of Georgia, Athens, Georgia 30602
2 Department of Mathematics, Princeton University, Princeton, New Jersey 08544
3 School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540 
@article{10_1090_S0894_0347_00_00357_X,
     author = {Granville, Andrew and Soundararajan, K.},
     title = {Large character sums},
     journal = {Journal of the American Mathematical Society},
     pages = {365--397},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2001},
     doi = {10.1090/S0894-0347-00-00357-X},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00357-X/}
}
TY  - JOUR
AU  - Granville, Andrew
AU  - Soundararajan, K.
TI  - Large character sums
JO  - Journal of the American Mathematical Society
PY  - 2001
SP  - 365
EP  - 397
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00357-X/
DO  - 10.1090/S0894-0347-00-00357-X
ID  - 10_1090_S0894_0347_00_00357_X
ER  - 
%0 Journal Article
%A Granville, Andrew
%A Soundararajan, K.
%T Large character sums
%J Journal of the American Mathematical Society
%D 2001
%P 365-397
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00357-X/
%R 10.1090/S0894-0347-00-00357-X
%F 10_1090_S0894_0347_00_00357_X
Granville, Andrew; Soundararajan, K. Large character sums. Journal of the American Mathematical Society, Tome 14 (2001) no. 2, pp. 365-397. doi: 10.1090/S0894-0347-00-00357-X

[1] Everett, C. J., Jr. Annihilator ideals and representation iteration for abstract rings Duke Math. J. 1939 623 627

[2] Burgess, D. A. The distribution of quadratic residues and non-residues Mathematika 1957 106 112

[3] Davenport, Harold Multiplicative number theory 1980

[4] Friedlander, J. B., Iwaniec, H. A note on character sums 1994 295 299

[5] Graham, S. W., Ringrose, C. J. Lower bounds for least quadratic nonresidues 1990 269 309

[6] Hildebrand, Adolf A note on Burgess’ character sum estimate C. R. Math. Rep. Acad. Sci. Canada 1986 35 37

[7] Hildebrand, Adolf, Tenenbaum, Gã©Rald Integers without large prime factors J. Théor. Nombres Bordeaux 1993 411 484

[8] Montgomery, Hugh L. An exponential polynomial formed with the Legendre symbol Acta Arith. 1980 375 380

[9] Montgomery, Hugh L. Ten lectures on the interface between analytic number theory and harmonic analysis 1994

[10] Montgomery, H. L., Vaughan, R. C. Exponential sums with multiplicative coefficients Invent. Math. 1977 69 82

[11] Pomerance, Carl On the distribution of round numbers 1985 173 200

[12] Tenenbaum, G. Cribler les entiers sans grand facteur premier Philos. Trans. Roy. Soc. London Ser. A 1993 377 384

Cité par Sources :