The Distribution of Values of Short Hybrid Exponential Sums on Curves over Finite Fields

Kit-Ho Mak, Alexandru Zaharescu

Type: Article

Publication Date: 2011-01-01

Citations: 6

DOI: https://doi.org/10.4310/mrl.2011.v18.n1.a12

Abstract

Let p be a prime number, X be an absolutely irreducible affine plane curve over Fp, and g, f ∈ Fp(x, y).We study the distribution of the values of the hybrid exponential sums Sn = Xon n ∈ I for some short interval I.We show that under some natural conditions the limiting distribution of the projections of the sum Sn, n ∈ I on any straight line through the origin is Gaussian as p tends to infinity.

Locations

Mathematical Research Letters - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (12)

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+	The distribution of rational points on varieties defined over a finite field	1981	Gerald Myerson
+	Estimation of a sum along an algebraic curve	1969	Г. И. Перельмутер
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+	Distribution of Selmer groups of quadratic twists of a family of elliptic curves	2008	Maosheng Xiong Alexandru Zaharescu
+ PDF Chat	GAUSSIAN LAWS ON DRINFELD MODULES	2009	Wentang Kuo Yu-Ru Liu
+	Distribution of rational points on varieties over finite fields	1988	Masahiko Fujiwara
+	The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions	1940	Péter L. Erdős Mark Kac
+	On Exponential Sums in Finite Fields	1966	Enrico Bombieri
+ PDF Chat	On the Distribution of the Number of Prime Factors of Sums a + b	1987	P. Erdos H. Maier Andràs Sárközy