Abstract
We define the p -density of a finite subset D ⊂ N r , and show that it gives a sharp lower bound for the p -adic valuations of the reciprocal roots and poles of zeta functions and L -functions associated to exponential sums over finite fields of characteristic p . When r = 1 , the p -density of the set D is the first slope of the generic Newton polygon of the family of Artin–Schreier curves associated to polynomials with their exponents in D .
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