New bounds for exponential sums with a non-degenerate phase polynomial
نویسندگان
چکیده
منابع مشابه
Bounds 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) ≡...
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15 صفحه اولSome tight polynomial-exponential lower bounds for an exponential function
This note is devoted to new sharp lower bounds for exp(x). We first introduce and study a new lower bound defined with polynomial of degree 2 and exponential (or hyperbolic) functions. Then we propose two improvements of this lower bound by using two different approaches; the first approach consists in adding well-chosen polynomial term to it, whereas the second approach aims to transform it fo...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2019
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2019.01.015