Geodesic
$p$-ADIC FORMAL SERIES AND COHEN'S PROBLEM
Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 47-61

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DOI

With the help of some $p$-adic formal series over $p$-adic number fields and the estimates of character sums over Galois rings, we prove that there is a constant $C(n)$ such that there exists a primitive polynomial $f(x)\,{=}\,x^{n}-a_{1}x^{n-1}+\cdots +(-1)^{n}a_{n}$ of degree $n$ over $F_{q}$ with the first $m=\lfloor\frac{n-1}{2}\rfloor$ coefficients $a_{1},\ldots ,a_{m}$ prescribed in advance if $q\,{>}\,C(n)$.
DOI : 10.1017/S0017089503001526
Mots-clés : 11T55, 11F85, 11L40 
SHUQIN, FAN; WENBAO, HAN. $p$-ADIC FORMAL SERIES AND COHEN'S PROBLEM. Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 47-61. doi: 10.1017/S0017089503001526
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     title = {$p${-ADIC} {FORMAL} {SERIES} {AND} {COHEN'S} {PROBLEM}},
     journal = {Glasgow mathematical journal},
     pages = {47--61},
     year = {2004},
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     doi = {10.1017/S0017089503001526},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001526/}
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