Related papers: Quadratic reciprocity in a finite group

We study the polygamy property for tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a lower bound of the set, which can be a sufficient and necessary…

We study rationality problem for the quotient of $\mathbb{C}^4$ by a finite primitive group $G$ of Type (I). We prove that this quotient is a rational variety for any such $G$.

We describe the development of a theoretical description of the structure of finite nuclei based on a relativistic quark model of the structure of the bound nucleons which interact through the (self-consistent) exchange of scalar and vector…

We construct a family of ideals representing ideal classes of order 2 in quadratic number fields and show that relations between their ideal classes are governed by certain cyclic quartic extensions of the rationals.

Let $\boldsymbol{\alpha}\in \mathbb{R}^N$ and $Q\geq 1$. We consider the sum $\sum_{\boldsymbol{q}\in [-Q,Q]^N\cap\mathbb{Z}^N\backslash\{\boldsymbol{0}\}}\|\boldsymbol{\alpha}\cdot\boldsymbol{q}\|^{-1}$. Sharp upper bounds are known when…

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the `kneading sequence' of the polynomial. We then give recursive presentations by generators and…

We survey new results on finite groups of birational transformations of algebraic varieties.

Every finite group whose order is divisible by a prime $p$ has at least $2 \sqrt{p-1}$ conjugacy classes.

I use harmonic maps and minimal surfaces to study quadratic equations in groups.

We prove an analog of Lagrange's Theorem for continued fractions on the Heisenberg group: points with an eventually periodic continued fraction expansion are those that satisfy a particular type of quadratic form, and vice-versa.

We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.

We consider symbolic flows over finite alphabets and study certain kinds of repetitions in these sequences. Positive and negative results for the existence of such repetitions are given for codings of interval exchange transformations and…

In analogy with the classical group law on a plane cubic curve, we define a group law on a smooth plane tropical cubic curve. We show that the resulting group is isomorphic to $S^1$.

In this paper, we consider some generalized commutator equations in a finite group and show that the number of solutions of such equations are characters of that group. We also obtain explicit formula for this character, considering the…

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of alternating groups.

It is well known that when a prime $p$ is congruent to 1 modulo 4, the sum of the quadratic residues equals the sum of the quadratic nonresidues. In this note we give analogous results for the case where $p$ is congruent to 3 modulo 4.

In the paper new criteria of existence and conjugacy of Hall subgroups of finite groups are given.

Plots of quadratic residues display some features that are analyzed mathematically.