In a recent paper [11], R.E. Curto, S.H. Lee and J. Yoon asked the following question. Let A be subnormal operator, assume that A2 is quasinormal. Does it follow quasinormal? this paper, we answer question in affirmative. fact, prove more general result nth roots of quasinormal operators are Research on problem has led us to new criterion for semispectral measure half-line spectral, written ter...

For any field K, a field K(ζn) where ζn is a root of unity (of order n) is called a cyclotomic extension of K. The term cyclotomic means circle-dividing, and comes from the fact that the nth roots of unity divide a circle into arcs of equal length. We will see that the extensions K(ζn)/K have abelian Galois groups and we will look in particular at cyclotomic extensions of Q and finite fields. T...

We prove a version for motivic cohomology of Thomason’s theorem on Bott-periodic K-theory, namely, that for a field k containing the nth roots of unity, the mod n motivic cohomology of a smooth k-scheme agrees with mod n étale cohomology, after inverting the element in H(k, Z/n(1)) corresponding to a primitive nth root of unity.

The following twelve poster abstracts were presented at the ANTS-8 poster session.1 ANTS-8 was held at the Banff Centre in Banff, Alberta Canada, May 17–22, 2008. The conference website, where many of the posters can be viewed online, is http://ants.math. ucalgary.ca/. Calculating Really Big Cyclotomic Polynomials Andrew Arnold and Michael Monagan, Simon Fraser University, ada26@ sfu.ca The nth...

The following twelve poster abstracts were presented at the ANTS-8 poster session.1 ANTS-8 was held at the Banff Centre in Banff, Alberta Canada, May 17–22, 2008. The conference website, where many of the posters can be viewed online, is http://ants.math. ucalgary.ca/. Calculating Really Big Cyclotomic Polynomials Andrew Arnold and Michael Monagan, Simon Fraser University, ada26@ sfu.ca The nth...

We give upper and lower bounds on the count of positive integers n x dividing the nth term of a non-degenerate linearly recurrent sequence with simple roots.

Let Ψn(x) be the monic polynomial having precisely all non-primitive nth roots of unity as its simple zeros. One has Ψn(x) = (x n − 1)/Φn(x), with Φn(x) the nth cyclotomic polynomial. The coefficients of Ψn(x) are integers that like the coefficients of Φn(x) tend to be surprisingly small in absolute value, e.g. for n < 561 all coefficients of Ψn(x) are ≤ 1 in absolute value. We establish variou...