Open AccessOn Fixed Divisors of Forms in Many Variables, I
Author(s) -
Andrzej Schinzel
Publication year - 2014
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-17104
Subject(s) - mathematics , divisor (algebraic geometry) , degree (music) , combinatorics , pure mathematics , discrete mathematics , physics , acoustics
Let $D_{d,r}$ be the maximal fixed divisor of a primitive form of degree $d$ in $r$ variables over $\mathsf{Z}$. A formula is given for $D_{d,2}$ and estimates for $D_{d,r}$ for $r>2$. As a consequence, a question of Nagell raised in 1919 is completely answered.