MOMENT ESTIMATES FOR EXPONENTIAL SUMS OVER k-FREE NUMBERS
نویسندگان
چکیده
منابع مشابه
Estimates for “Singular” Exponential Sums
In [D1, Thm. 8.4], Deligne proved the following beautiful estimate for exponential sums in n ≥ 1 variables. Given a polynomial f(x1, . . . , xn) in n variables over k of some degree d ≥ 1, write it as f = Fd + Fd−1 + · · · F0 with Fi homogeneous of degree i. Suppose that the following two conditions are satisfied. (1) The degree d is prime to p := char(k). (2) The locus Fd = 0 is a nonsingular ...
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1Many of the manipulations of sums in these chapters are hard to follow, and I greatly expand on the calculations in Davenport. The organization of the proof in Davenport seems to be due to Vaughan. I have also used lecture notes by Andreas Strömbergsson, http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf, pp. 245–257. Another set of notes, which I have not used, are http://jonismathnote...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2013
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042112501515