Related papers: A counterexample to 'Algebraic function fields wit…

We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action…

We show that a class of Dirichlet series ${\mathfrak{A}}^{\#}$ that is much larger than the extended Selberg class ${\mathscr{S}}^{\#}$, and also contains the standard as well as the tensor product, exterior square and symmetric square…

In this short note we prove by a counter-example that Theorem 3.2 in the paper "A study on concave optimization via canonical dual function" by J. Zhu, S. Tao, D. Gao is false; moreover, we give a very short proof for Theorem 3.1 in the…

In this short note we present a family of counterexamples to the King's conjecture.

Let $G$ be a finite group and $\alpha(G)=\frac{|C(G)|}{|G|}$\,, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $\alpha(G)\leq\alpha(Z(G))$ and we describe the groups $G$ for which the equality…

This note collects several results on the capability of $p$-groups of class two and prime exponent. Among the new results, we settle the 4-generator case for this class.

We prove that any 2-generated minimal Taylor algebra on a domain of size 4 is not simple. In addition, we find all such algebras up to isomorphism and term-equivalence.

We prove the local Langlands correspondence for GSp_4(F), where F is a non-archimedean local field of positive characteristic with residue characteristic > 2.

We give counterexamples for the modification on Malle's Conjecture given by T\"urkelli. T\"urkelli's modification on Malle's conjecture is inspired by an analogue of Malle's conjecture over a function field. As a consequence, our…

A class of rational functions characterized by some wonderful properties is studied. The properties that identify this class include simple algebra (their inverses can be expressed in radicals), simple topology (the total space of the…

Let P be a distinguished unary predicate and K= {M: M a model of cardinality aleph_n with P^M of cardinality aleph_0}. We prove that consistently for n=4, for some countable first order theory T we have: T has no model in K whereas every…

A representation field for a non-maximal order H in a central simple algebra A is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders representing H. In our previous work we…

The theory of continued fractions of functions $ \sqrt D $ is used to give lower bound for class numbers $h(D)$ of general real quadratic function fields $K=k(\sqrt D)$ over $k={\bf F}_q(T)$. For five series of real quadratic function…

Let $p$ be a prime integer and $F$ the function field in two algebraically independent variables over a smaller field $F_0$. We prove that if $\operatorname{char}(F_0)=p\geq 3$ then there exist $p^2-1$ cyclic algebras of degree $p$ over $F$…

This paper discusses a function that is frequently presented as a simile or look-alike of the so-called ``counterexample function to P=NP,'' that is, the function that collects all first instances of a problem in NP where a poly machine…

Let $K$ be a global function field together with a place $\infty$, and $A$ the subring of functions regular outside $\infty$. In this paper we present an effective method to evaluate the (locally free) class number of an arbitrary…

We will give a simple proof of the ambiguous class number formula.

We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions…

We say that an algebraic group $G$ over a field is anti-affine if every regular function on $G$ is constant. We obtain a classification of these groups, with applications to the structure of algebraic groups in positive characteristics, and…

We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…