Related papers: About the Kronecker Theorem
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by…
We consider generalizations of Gale's colored KKM lemma and Shapley's KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions.
The recent discovery of light moving backwards in time, when it propagates in a suitable dispersive medium, obliges us to reexamine the Kramers-Kronig relations. In their usual form, they are dealing with usual light (moving forward in…
We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a unique turning point in…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
This paper is withdrawn. We found a mistake in Lemma 4.1
We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring $R[X]$, over a commutative ring $R$ in which 2 is invertible, as a product of an…
Hadamard's global inverse theorem provides conditions for a function to be globally invertible on Rn. In this note we show that the conditions are robust enough for the conclusion to hold even if we relax the conditions by removing the…
We prove an analogue of Clifford's inequality for tropical curves. Next we focus on the hyperelliptic case and we characterize divisors attaining equality. Finally we speculate whether inequality in tropical Clifford's Theorem does imply…
We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of…
Kronecker observed that either all roots or only one root of a solvable irreducible equation of odd prime degree with integer coefficients are real. This gives a possibility to construct specific examples of equations not solvable by…
This paper has been withdrawn by the authors due to an error in Section 7.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We discuss the (twisted) weak positivity theorem. We also treat some applications.
In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric…
We prove a general version of the "Stability Theorem": if $K$ is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if $F|K$ is a finitely generated (transcendental) extension of…
We provide a simple proof of Kamp's theorem.
In this paper we give sufficient conditions for a compactum in $\mathbb R^n$ to have Carath\'{e}odory number less than $n+1$, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath\'{e}odory…
We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, topological dynamics and combinatorics.
The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…