The p-adic limits of iterated p-power cyclic resultants of multivariable polynomials

2025/03/08 by Yoshizaki, Hyuga
#11C08 #11R09 #13P15 #57K10 #57K31 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.06194

Abstract

Let p be a prime number. The p-power cyclic resultant of a polynomial is the determinant of the Sylvester matrix of t^pn-1 and the polynomial. It is known that the sequence of p-power cyclic resultants and its non-p-parts converge in ℤ_p. This article shows the p-adic convergence of the iterated p-power cyclic resultants of multivariable polynomials. As an application, we show the p-adic convergence of the torsion numbers of ℤ_p^d-coverings of links. We also explicitly calculate the p-adic limits for the twisted Whitehead links as concrete examples. Moreover, in a specific case, we show that our p-adic limit of torsion numbers coincides with the p-adic torsion, which is a homotopy invariant of a CW-complex introduced by S. Kionke.

Related

• The p-adic limits of class numbers in ℤ_p-towers
• The Iwasawa invariants of ℤ_p ^d-covers of links
• p-adic families of diagonal cycles
• Bounds on torsion of CM abelian varieties over a p-adic field with values in a field of p-power roots
• Arithmetic invariants of torus links