p-adic variation of L-functions of exponential sums, I

Details p-adic variation of L-functions of exponential sums, I p-adic variation of L-functions of exponential sums, I

2001-11-18

arxiv.org/abs/math/0111194v1

American Journal of Mathematics 125 (2003), 669-690.

Mathematics

Algebraic Geometry

18 pages, LaTeX

Scientific paper

For a polynomial f(x) in (Z_p\cap Q)[x] of degree d>2 let L(f mod p;T) be the L-function of the exponential sum of f mod p. Let NP(f mod p) denote the Newton polygon of L(f mod p;T). Let HP(f) denote the Hodge polygon of f, which is the lower convex hull in the real plane of the points (n,n(n+1)/(2d)) for 0\leq n\leq d-1. We prove that there is a Zariski dense subset U defined over Q in the space A^d of degree-d monic polynomials over Q such that for all f in U(Q) we have lim NP(f mod p) = HP(f) as p approaches infinity. Moreover, we determine the p-adic valuation of every coefficient of L(f mod p;T) for p large enough and f in U(Q).

Affiliated with

Also associated with

No associations

Rating

p-adic variation of L-functions of exponential sums, I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with p-adic variation of L-functions of exponential sums, I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and p-adic variation of L-functions of exponential sums, I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-231214