Exponential sums and the abelian group problem
نویسندگان
چکیده
منابع مشابه
Translation invariance, exponential sums, and Waring’s problem
We describe mean value estimates for exponential sums of degree exceeding 2 that approach those conjectured to be best possible. The vehicle for this recent progress is the efficient congruencing method, which iteratively exploits the translation invariance of associated systems of Diophantine equations to derive powerful congruence constraints on the underlying variables. There are application...
متن کاملBounds on Exponential Sums and the Polynomial Waring Problem Mod
Estimates are given for the exponential sum ∑p x=1 exp(2πif(x)/p), p a prime and f a nonzero integer polynomial, of interest in cases where the Weil bound is worse than trivial. The results extend those of Konyagin for monomials to a general polynomial. Such bounds readily yield estimates for the corresponding polynomial Waring problem mod p, namely the smallest γ such that f(x1)+ . . .+f(xγ) ≡...
متن کاملA problem related to the divisibility of exponential sums
Francis Castro, et al computed the exact divisibility of families of exponential sums associated to binomials F (X) = aX1 + bX2 over Fp, and a conjecture is presented for related work. Here we study this question.
متن کاملDiophantineMethods for Exponential Sums, and Exponential Sums for Diophantine Problems
Recent developments in the theory and application of the HardyLittlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of exponential sums are described first, concentrating on developments involving smooth Weyl sums. Next, arithmetic variants of classical inequalities of Bessel and ...
متن کاملExponential Sums
where we in introduce the standard notation e(x) = exp(2πix). Question 1.1. What is the magnitude of | ∑ x∈S e(x)|? By the trivial bound, we find that | ∑ x∈S e(x)| ≤ N , with equality whenever the terms are all equal. One can of course make the sum much smaller–simply sum the Nth roots of unity. In between these two extremes–completely in phase and maximally out of phase–we should consider wha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2010
ISSN: 0208-6573
DOI: 10.7169/facm/1277811635