The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

We give a necessary, and in some cases sufficient, condition for sliceness inside the family
of pretzel knots P (p 1,…, pn) with one pi even. The 3–stranded case yields two interesting …

Fekete polynomials associate with each prime number pa polynomial with coefficients− 1 or
1 except the constant term, which is 0. These coefficients reflect the distribution of quadratic …

Three proofs of an observation on irreducible polynomials over GF(2) - ScienceDirect Skip to
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In this paper, we establish some relations between irreducible polynomials over a finite field
F q and its quadratic extension F q 2. First we consider a relation between the numbers of …

We generalize Carlitzʼ result on the number of self-reciprocal monic irreducible polynomials
over finite fields by showing that similar explicit formula holds for the number of irreducible …

It is well known that the Stickelberger–Swan theorem is very important for determining the
reducibility of polynomials over a binary field. Using this theorem the parity of the number of …

The class of self-conjugate-reciprocal irreducible monic (SCRIM) polynomials over finite
fields are studied. Necessary and sufficient conditions for monic irreducible polynomials to …

We study the Poincaré polynomials of all known Calabi–Yau three-folds as constrained
polynomials of Littlewood type, thus generalising the wellknown investigation into the …

This paper is concerned with the restriction of interval exchange transformations (IETs) to
algebraic number fields, which leads to maps on lattices. We characterize renormalizability …