Related papers: The Heyde Theorem on a-adic Solenoids
In this short note, we introduce an Euler analogue of Wilson's theorem; $a_1a_2... a_{\phi(n)}\equiv (-1)^{\phi(n)+1}~({\rm mod}~n)$ say, where ${\rm gcd}(a_i,n)=1$.
In this paper, we present a short proof of Halin's grid theorem.
Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.
We sketch several proofs of F\'ary--Milnor theorem.
The purpose of this paper is to derive the analogue of Lebesgue-Radon-Nikodym theorem with respect to $p$-adic $q$-invariant distribution on $\Bbb Z_p$ which is defined by author in [1].
We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-etale site, which makes all constructions…
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
In this note we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple…
In this paper, we give a simple counter example to the famous Hodge conjecture.
We prove some symmetric $q$-congruences.
According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given another. In the article, we…
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study…
We establish a q-analogue of Wolstenholme's harmonic series congruence.
We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.
We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.
We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.
We prove several extensions of the Erdos-Fuchs theorem.
A p-adic analogue of the pseudonorm version of the birational Torelli type theorem is obtained via a comparison theorem of image closures. Among other results obtained, we have a criterion for existence of rational points of canonically…
We consider higher-dimensional analogues of the classical Brauer-Siegel theorem focusing on the case of abelian varieties over global function fields. We prove such an analogue in the case of constant families of elliptic curves and abelian…
We prove the analog of the Kac conjecture for hard sphere collisions