Related papers: Rational Quartic Reciprocity II
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
Rational twisted power series over a (commutative) field are studied. We give several characterizations of such series, which are similar to the classical results concerning rational power series over a commutative field. In particular, we…
The solvability of the cubic congruence $x^{3}\equiv 2\pmod{p}$ is referred to as the $\textit{cubic character of 2}$. In evaluating the cubic character of 2, we introduce the Eisenstein integers, Gauss and Jacobi sums, and the law of cubic…
We give a complete description of the qualitative behavior of the second-order rational difference equation #166. We also establish the boundedness character for the rational system in the plane #(8,30).
In this note, we find a new way to prove several properties of 2-alternating capacities.
We find conditions equivalent to some commutator identities considered in Part I
We study equivariant birational geometry of (rational) quartic double solids ramified over (singular) Kummer surfaces.
The Law of Quadratic Reciprocity was conjectured by Euler and Legendre who both found an incomplete proof. Gauss called this law "Theorema Fundamentale", and he was the first who gave a complete proof, he also highlighted the equivalence of…
We study rationality properties of real singular cubic threefolds.
Question when rectangle can be tiled with similar copies of rectangles witch quetient of sides quadratic irrationalities. New proof of one part F. Sharov's theorem. Other close result.
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
We sketch the construction of a derived enhancement of the reciprocity isomorphism of class field theory. Details will appear in a forthcoming joint paper of the authors with A. Raksit.
Several years ago, I suggested a quantum field theory which has many attractive features. (1) It can explain the quantization of electric charge. (2) It describes symmetrized Maxwell equations. (3) It is manifestly covariant. (4) It…
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
The article investigates several questions about field generated by certain formal group laws. This is continuation of a study initiated by the author in prior article titled 'Field Generated by Division Points of Certain Formal Group…
In this note let us give two remarks on proof-theory of PA. First a derivability relation is introduced to bound witnesses for provable $\Sigma_{1}$-formulas in PA. Second Paris-Harrington's proof for their independence result is…
In this article we show that the motive of an affine quadric {q = 1} determines the respective quadratic form.
In this small article, unified first law has been analyzed and some results have been deduced from it. The results have been presented in the form of lemmas and some conclusions have been drawn from them.
This paper considers three different partition relations from partition calculus, two of which are pair relations and one of which is a triple relation. An examination of the first partition relation and the ramification argument used to…
An introduction is given to the Littlewood-Richardson rule, and various combinatorial constructions related to it. We present a proof based on tableau switching, dual equivalence, and coplactic operations. We conclude with a section…