Kavli Affiliate: Kinfai Mak
| First 5 Authors: Kit-Ho Mak, Kit-Ho Mak, , ,
| Summary:
Let $p$ be a prime number, $C$ be any absolutely irreducible affine plane curve over $mathbbF_p$, and $g,finmathbbF_p(x,y)$ be rational functions. We continue the study of the distribution of the values of short hybrid exponential sums of the form $S_H(x;C) = sum_Pin C, x<x(P)leq x+Hχ(g(P))ψ(f(P))$ on $xinmathcalI$ for some short interval $mathcalI$. We show that under some natural conditions, the limiting distribution of the sum $S_H(x;C)$ is Gaussian for all curve $C$. This largely generalizes a previous result of the author and Zaharescu.
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