3120

3077

كارشناسي ارشد

﴿رياضي محض﴾

اصفهان،دانشگاه صنعتي اصفهان،دانشكده علوم رياضي

1385

[الف]،هفت،121،[II]ص.

ص.ع.به فارسي و انگليسي

بيژن طائري

عاطفه قرباني

انگليسي به فارسي

عليرضا اشرفي، رضا ودادي

رياضي

ID3077

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

AbstractLet Fq denote the finite field of q elements q an odd prime power Using the estimates of character sums over Fq and Cohen stechniques we prove that there always exists a primitive polynomialof degree n over Fq q odd with the first and second coefficientsprescribed in advanced when n 7 Then we make some neededmodifications to case n 7 resolve the cases n 5 6 in the affirmative and discuss the case n 4 as well Then Using the estimates of character sums over Galois rings andCohen s sieve we prove that there exists a primitive polynomial overFq of degree n with the first three coefficients prescribed when n 8 Then resolves the n 7 case for finite fields of characteristic at least 5 Finally we deal with the remaining cases and prove that there exists aprimitive polynomial of degree 7over Fq with the first three coefficient prescribed where thecharacteristic of Fq is 2 or 3

بيژن طائري

عاطفه قرباني

عليرضا اشرفي، رضا ودادي