Monogenic Pisot and Anti-Pisot Polynomials

Monogenity and Power Integral Bases: Recent Developments

“…• H. H. Kim [139] showed that the number of monogenic dihedral quartic extensions with absolute discriminant ≤ X is of size O(X 3/4 (log X) 3 ) • N. Khan, S. Katayama, T. Nakahara and T. Uehara [137] proved that the composite of a totally real field with a cyclotomic field of odd conductor ≥ 3 or even ≥ 8 has no power integral basis • N. Khan, T. Nakahara and H. Sekiguchi [136] proved that there are exactly three monogenic cyclic sextic fields of prime-power conductor, namely Q(ζ 7 ), Q(ζ 9 ) and the maximal real subfield of Q(ζ 13 ) • D. Gil-Mu noz and M. Tinková [81] considered the indices of non-monogenic simplest cubic polynomials • L. Jones [122] considered infinite families of monogenic Pisot (anti-Pisot) polynomials • A. Jakhar and S. K. Khanduja [98] gave lower bounds for the p-index of a polynomial • M. Castillo, [25] showed e.g. that Q(α n ), n ≥ 1 is monogenic, where α 0 = 1 and α n = √ 2 + α n−1 for n ≥ 1 • T. Kashio and R. Sekigawa [133] showed that a monogenic normal cubic field is a simplest cubic field for some parameter • F. E. Tanoé [153] considered monogenity of biquadratic fields using a special integer basis • K. V. Kouakou and F. E. Tanoé [140], [154] and F. E. Tanoé and V. Kouassi [155] considered monogenity of triquadratic fields • Aruna C. and P. Vanchinathan [7] showed that an infinite number of so called exceptional quartic fields are monogenic…”

Monogenity and Power Integral Bases: Recent Developments

“…• D. Gil-Mu noz and M. Tinková [131] considered the indices of non-monogenic simplest cubic polynomials; • L. Jones [132] considered infinite families of monogenic Pisot (anti-Pisot) polynomials; • A. Jakhar and S. K. Khanduja [133] gave lower bounds for the p-index of a polynomial; • M. Castillo, [134] showed, e.g., that Q(α n ), n ≥ 1 is monogenic, where α 0 = 1 and…”