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- W2969809849 abstract "In this paper we establish function field versions of two classical conjectures on prime numbers. The first says that the number of primes in intervals (x,x+x^epsilon] is about x^epsilon/log x and the second says that the number of primes p 1 and mgeq 3 if q is even and deg f' leq 1. We show that this estimation fails in the neglected cases. Let pi_q(k) be the number of monic prime polynomials of degree k with coefficients in the finite field with q elements FF_q. For relatively prime polynomials f,Din FF_q[t] we prove that the number N' of monic prime polynomials g that are congruent to f modulo D and of degree k satisfies |N'-pi_q(k)/phi(D)|leq c(k)pi_q(k)q^{-1/2}/phi(D), as long as 1leq ° Dleq k-3 (or leq k-4 if p=2 and (f/D)' is constant). We also generalize these results to other factorization types." @default.
- W2969809849 created "2019-08-29" @default.
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- W2969809849 date "2013-02-04" @default.
- W2969809849 modified "2023-09-27" @default.
- W2969809849 title "Prime polynomials in short intervals over large finite fields" @default.
- W2969809849 hasPublicationYear "2013" @default.
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