p-ADIC FORMAL SERIES AND PRIMITIVE POLYNOMIALS OVER FINITE FIELDS
نویسندگان
چکیده
In this paper, we investigate the Hansen-Mullen conjecture with the help of some formal series similar to the Artin-Hasse exponential series over p-adic number fields and the estimates of character sums over Galois rings. Given n we prove, for large enough q, the Hansen-Mullen conjecture that there exists a primitive polynomial f(x) = xn − a1xn−1 + · · ·+ (−1)an over Fq of degree n with the m-th (0 < m < n) coefficient am fixed in advance except when m = n+1 2 if n is odd and when m = n 2 , n 2 + 1 if n is even.
منابع مشابه
GENERALISED HEEGNER CYCLES AND p-ADIC RANKIN L-SERIES
Introduction 2 1. Preliminaries 6 1.1. Algebraic modular forms 6 1.2. Modular forms over C 9 1.3. p-adic modular forms 11 1.4. Elliptic curves with complex multiplication 12 1.5. Values of modular forms at CM points 14 2. Generalised Heegner cycles 15 2.1. Kuga-Sato varieties 15 2.2. The variety Xr and its cohomology 18 2.3. Definition of the cycles 19 2.4. Relation with Heegner cycles and L-se...
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