33 citations · 53 across the 22 of their papers we have counts for
18 papers · 1 filter
Cyclotomic factors of rational necklace functions
Nguyen Cao Minh, Nguyen Vu Hoang Minh, Dung Nguyen +3
Necklace polynomials arise in various fields of mathematics, including combinatorics, Lie theory, and Galois theory over finite fields. Their arithmetic properties have been extens…
Supercharacters of finite abelian groups and applications to spectra of -unitary Cayley graphs
Tung T. Nguyen, Nguyen Duy Tân
We define super-Cayley graphs over a finite abelian group . Using the theory of supercharacters on , we explain how their spectra can be realized as a super-Fourier transform…
On gcd-graphs over finite rings
Tung T. Nguyen, Nguyen Duy Tân
Gcd-graphs represent an interesting and historically important class of integral graphs. Since the pioneering work of Klotz and Sander, numerous incarnations of these graphs have b…
Isomorphic gcd-graphs over polynomial rings
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
Gcd-graphs over the ring of integers modulo are a simple and elegant class of integral graphs. The study of these graphs connects multiple areas of mathematics, including graph…
Fekete polynomials of principal Dirichlet characters
Shiva Chidambaram, Ján Mináč, Tung T. Nguyen +1
Fekete polynomials associated to quadratic Dirichlet characters have interesting arithmetic properties, and have been studied in many works. In this paper, we study a seemingly sim…
On the arithmetic of generalized Fekete polynomials
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
For each prime number one can associate a Fekete polynomial with coefficients or except the constant term, which is 0. These are classical polynomials that have been s…
Galois module structure of some elementary -abelian extensions
Lauren Heller, Jan Minac, Tung T. Nguyen +2
We determine the Galois module structure of the parameterizing space of elementary -abelian extensions of a field when is any finite -group, under the a…
Quaternion algebras and square power classes over biquadratic extensions
Frank Chemotti, Jan Minac, Tung T. Nguyen +3
Recently the Galois module structure of square power classes of a field has been computed under the action of in the case where is the Klein…
Fekete polynomials, quadratic residues, and arithmetic
Jan Minac, Tung T. Nguyen, Nguyen Duy Tan
Fekete polynomials associate with each prime number a polynomial with coefficients or except the constant term, which is 0. These coefficients reflect the distribution…
Further insights into the mysteries of the values of zeta functions at integers
Ján Mináč, Nguyen Duy Tân, Nguyen Tho Tung
We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to a…
Description of Galois unipotent extensions
Masoud Ataei, Jan Minac, Nguyen Duy Tan
Given an arbitrary field , we describe all Galois extensions whose Galois groups are isomorphic to the group of upper triangular unipotent 4-by-4 matrices with entries in…
Construction of unipotent Galois extensions and Massey products
Jan Minac, Nguyen Duy Tan
For all primes and all fields, we find a sufficient and necessary condition of the existence of a unipotent Galois extension of degree . The main goal of this paper is to…
Triple Massey products vanish over all fields
Jan Minac, Nguyen Duy Tan
We show that the absolute Galois group of any field has the vanishing triple Massey product property. Several corollaries for the structure of maximal pro--quotient of absolute…
Counting Galois -extensions using Massey products
Jan Minac, Nguyen Duy Tan
We use Massey products and their relations to unipotent representations to parametrize and find an explicit formula for the number of Galois extensions of a given local field with…
Triple Massey products over global fields
Jan Minac, Nguyen Duy Tan
Let be a global field which contains a primitive -th root of unity, where is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for , any triple Massey…
The Kernel Unipotent Conjecture and the vanishing of Massey products for odd rigid fields
Jan Minac, Nguyen Duy Tan, Ido Efrat
A major difficult problem in Galois theory is the characterization of profinite groups which are realizable as absolute Galois groups of fields. Recently the Kernel -Unipotent C…
Triple Massey products and Galois theory
Jan Minac, Nguyen Duy Tan
We show that any triple Massey product with respect to prime 2 contains 0 whenever it is defined over any field. This extends the theorem of M. J. Hopkins and K. G. Wickelgren, fro…
On Galois cohomology of unipotent algebraic groups over local fields
Nguyen Duy Tan
In this paper, we give a necessary and sufficient condition for the finiteness of Galois cohomology of unipotent groups over local fields of positive characteristic