LARGE VALUES OF FOR TH ORDER CHARACTERS AND APPLICATIONS TO CHARACTER SUMS
نویسندگان
چکیده
منابع مشابه
FINITE FIELDS AND APPLICATIONS Characters and character sums (9 lectures)
Exponential sums and character sums have many applications in number theory and combinatorial number theory. Many famous and interesting problems have been studied by means of exponential sums techniques: Goldbach ternary conjecture (Vinogradov), Waring Problem (Hardy, Littlewood, Vaughan, Vinogradov, Wooley), Distribution of prime numbers (Ford, Hardy, Korobov, Linnik,...) as well as many othe...
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There has been no subsequent improvement in this inequality other than in the implicit constant. Moreover it is believed that (1.1) will be difficult to improve since it is possible (though highly unlikely) that there is an infinite sequence of primes q ≡ 3 (mod 4) for which (pq ) = 1 for all p < q , in which case M(( · q )) √ q log q. The unlikely possibility described above involves a quadrat...
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where χ is a non-principal Dirichlet character χ (mod q). It is easy to show that such character sums are always ≤ q in absolute value, while G. Pólya and I.M. Vinogradov (see [3]) improved this to≤ √q log q around 1919, and H.L. Montgomery and R.C. Vaughan [13] to √q log log q in 1977, assuming the Generalized Riemann Hypothesis (GRH). Up to the constant this is “best possible” since R.E.A.C. ...
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ژورنال
عنوان ژورنال: Mathematika
سال: 2016
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579316000164