Related papers: A Direct Proof of Landen's Transformation
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…
We prove a uniformization theorem in complex algebraic geometry.
We present an astonishingly simple and elegant proof of the celebrated Basel problem.
In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.
We prove an infinitary version of the Brauer-Schur theorem.
The aim of this short note is to provide a very simple proof for obtaining the fundamental two-term transformation for the series ${}_3F_2(1)$ due to Thomae.
In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.
We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordinary differential equation that admits Bernoulli equation as…
We prove the Yoneda lemma inside an elementary higher topos, generalizing the Yonda lemma for spaces.
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
Linearization of coupled second order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper we describe a simple and straightforward method to…
In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…
We prove the splitting of the Kummer exact sequence and related exact sequences in arithmetic geometry.
In this paper, a direct proof is presented for a case of a Malmsten integral. The method used in solving the integral is a direct one that the author has not come accross in any old or recent publication. Integration by parts, Laplace…
In this short paper we present an elementary proof of the infinitude of primes. Our proof is similar in spirit to Euler's proof that the reciprocals of primes diverges and only uses tools from elementary number theory and calculus. In…
We proved that there are infinitely many cousin primes.
We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.
We summarize and extend E. Moody's results on the explicit equations related to the Bertini involution.
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
Several infinite products are studied that satisfy the transformation relation of the type $f(\alpha)=f(1/\alpha)$. For certain values of the parameters these infinite products reduce to modular forms. Finite counterparts of these infinite…