20.500.12556/RUL-161817 Ciklotomični polinomi delo diplomskega seminarja Cyclotomic polynomials Ciklotomične polinome vpeljemo kot minimalne polinome primitivnih korenov enote nad poljem racionalnih števil. Pokažemo, da imajo celoštevilske koeficiente, ki jih v nadaljevanju obravnavamo bolj podrobno. Med drugim zanje poiščemo eksplicitno formulo, ki nas vodi do nekaterih integralskih identitet. Obravnavamo lastnosti koeficientov $n$-tega ciklotomičnega polinoma glede na praštevilsko faktorizacijo števila $n$. Z uvedbo alternativne definicije ciklotomičnih polinomov pokažemo, da so njihovi koeficienti neomejeni. S pomočjo ciklotomičnih polinomov dokažemo Wedderburnov mali izrek. We introduce cyclotomic polynomials as minimal polynomials of primitive roots of unity over the field of rational numbers. We show that they have integer coefficients, which are the subject of further analysis. Among other things we find their form through explicit formulas which leads us to some integral identities. We consider the properties of the coefficients of the $n$-th cyclotomic polynomial based on the prime factorization of the number $n$. By introducing an alternative definition of cyclotomic polynomials we prove that their coefficients have no upper bound. Using cyclotomic polynomials we prove Wedderburn’s little theorem. ciklotomični polinomi minimalni polinomi koreni enote koeficienti cyclotomic polynomials minimal polynomials roots of unity coefficients true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2024-09-14 08:15:41 2024-09-14 08:15:42 2024-09-18 09:38:40 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 143356 207975939 12901.pdf 12901.pdf 1 87DE1D08A2A89332D7BD43D35D39FAEA 60655a70840b55a238919fc2a09538b06562714167eb48089138040cb6238717 b1dc6984-7260-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190801 Fakulteta za matematiko in fiziko 0 0 0