Article ID Journal Published Year Pages File Type
4583082 Finite Fields and Their Applications 2010 10 Pages PDF
Abstract

In 1901, von Koch showed that the Riemann Hypothesis is equivalent to the assertion that∑p⩽xpprime1=∫2xdtlogt+O(xlogx). We describe an analogue of von Koch's result for polynomials over a finite prime field FpFp: For each natural number n, write n in base p, sayn=a0+a1p+⋯+akpk,n=a0+a1p+⋯+akpk, and associate to n   the polynomial a0+a1T+⋯+akTk∈Fp[T]a0+a1T+⋯+akTk∈Fp[T]. We let πp(X)πp(X) denote the number of irreducible polynomials encoded by integers n

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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