Related papers: A Note on Cyclotomic Integers

We determine higher topological Hochschild homology of rings of integers in number fields with coefficients in suitable residue fields. We use the iterative description of higher THH for this and Postnikov arguments that allow us to reduce…

We study the cone of effective divisors and the total coordinate ring of wonderful varieties, with applications to their automorphism group. We show that the total coordinate ring of any spherical variety is obtained from that of the…

We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counting isomorphism classes of absolutely irreducible…

It is proved that the ring of invariants of the standard smooth completion of a Kac-Moody Lie algebra is functionally generated by two elements: the coefficient of the center and the Killing form.

We use the spectral theory of Hilbert-Maass forms for real quadratic fields to obtain the asymptotics of some sums involving the number of representations as a sum of two squares in the ring of integers.

The problem of expressing an element of K_2(F) in a more explicit form gives rise to many works. To avoid a restrictive condition in a work of Tate, Browkin considered cyclotomic elements as the candidate for the element with an explicit…

In this article we prove, in a simple way, that for any complete toric variety, and for any Cartier divisor, the ring of global sections of multiples of the line bundle associated to the divisor is finitely generated.

With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite fields. Also, we confirm some related conjectures posed by…

In this article it is determined which integral reflection representations of the symmetric groups and the primitive complex reflection groups of degree $2$ have rings of invariants which are isomorphic to polynomial rings.

In earlier work we developed the theory of signatures of hermitian forms over algebras with involution with respect to orderings on the base field of the algebra and obtained in particular that the total signature of a hermitian form is a…

We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.

Consider the Grothendieck group of finite type projective modular representations of the symmetric groups on n letters, or more generally, of its wreath product with a finite group. They form a graded group, with a product defined using…

We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values. In order to perform these simplifications, we view the series as…

Sylvester showed that the partition of an integer into a set of positive integers can be represented as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. The wave itself is a weighted sum of the…

We make a list of finite simple groups whose group rings over a given field are serial.

A finite set of integers $A$ tiles the integers by translations if $\mathbb{Z}$ can be covered by pairwise disjoint translated copies of $A$. Restricting attention to one tiling period, we have $A\oplus B=\mathbb{Z}_M$ for some…

We describe Greenberg's pseudo-null conjecture, and prove a result describing conditions under which the pseudo-null conjecture for a number field $K$ implies the conjecture for finite extensions of $K$. We then apply the result to the…

We show how to determine if a given simple rectilinear polygon can be tiled with rectangles, each having an integer side.

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

In the mid 80's Conner and Perlis showed that for cyclic number fields of prime degree $p$ the isometry class of integral trace is completely determined by the discriminant. Here we generalize their result to tame cyclic number fields of…