Geodesic
Large character sums: Pretentious characters and the Pólya-Vinogradov theorem
Granville, Andrew1 ; Soundararajan, K.2, 3
1 Département de Mathématiques et Statistique, Université de Montréal, CP 6128 succ Centre-Ville, Montréal, Quebec H3C 3J7, Canada
2 Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
3 Department of Mathematics, Stanford University, Building 380, 450 Serra Mall, Stanford, California 94305-2125
Journal of the American Mathematical Society, Tome 20 (2007) no. 2, pp. 357-384

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

In 1918 Pólya and Vinogradov gave an upper bound for the maximal size of character sums, which still remains the best known general estimate. One of the main results of this paper provides a substantial improvement of the Pólya-Vinogradov bound for characters of odd, bounded order. In 1977 Montgomery and Vaughan showed how the Pólya-Vinogradov inequality may be sharpened assuming the Generalized Riemann Hypothesis. We give a simple proof of their estimate and provide an improvement for characters of odd, bounded order. The paper also gives characterizations of the characters for which the maximal character sum is large, and it finds a hidden structure among these characters.
DOI : 10.1090/S0894-0347-06-00536-4

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

1 Département de Mathématiques et Statistique, Université de Montréal, CP 6128 succ Centre-Ville, Montréal, Quebec H3C 3J7, Canada
2 Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
3 Department of Mathematics, Stanford University, Building 380, 450 Serra Mall, Stanford, California 94305-2125 
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Granville, Andrew; Soundararajan, K. Large character sums: Pretentious characters and the Pólya-Vinogradov theorem. Journal of the American Mathematical Society, Tome 20 (2007) no. 2, pp. 357-384. doi: 10.1090/S0894-0347-06-00536-4

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