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This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials.
Arnold Adelberg, and Michael Filaseta. "On mth order Bernoulli polynomials of degree m that are Eisenstein." Colloquium Mathematicae 93.1 (2002): 21-26. <http://eudml.org/doc/284760>.
@article{ArnoldAdelberg2002, abstract = {This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials.}, author = {Arnold Adelberg, Michael Filaseta}, journal = {Colloquium Mathematicae}, keywords = {Bernoulli polynomials; Bernoulli numbers; irreducibility of polynomials; Eisenstein polynomials}, language = {eng}, number = {1}, pages = {21-26}, title = {On mth order Bernoulli polynomials of degree m that are Eisenstein}, url = {http://eudml.org/doc/284760}, volume = {93}, year = {2002}, }
TY - JOUR AU - Arnold Adelberg AU - Michael Filaseta TI - On mth order Bernoulli polynomials of degree m that are Eisenstein JO - Colloquium Mathematicae PY - 2002 VL - 93 IS - 1 SP - 21 EP - 26 AB - This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials. LA - eng KW - Bernoulli polynomials; Bernoulli numbers; irreducibility of polynomials; Eisenstein polynomials UR - http://eudml.org/doc/284760 ER -