Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Ghosh, Arkabrata"'
The study of symmetric structures is a new trend in Ramsey theory. Recently in [7], Di Nasso initiated a systematic study of symmetrization of classical Ramsey theoretical results, and proved a symmetric version of several Ramsey theoretic results. I
Externí odkaz:
http://arxiv.org/abs/2404.04502
Autor:
Ghosh, Arkabrata
In this article, we consider a family of elliptic curves defined by $E_{m}: y^2= x^3 -m^2 x + (pqr)^2 $ where $m $ is a positive integer and $p, q, ~\text{and}~ r$ are distinct odd primes and study the torsion as well the rank of $E_{m}(\mathbb{Q})$.
Externí odkaz:
http://arxiv.org/abs/2403.01213
Autor:
Ghosh, Arkabrata
In this article, we consider primes $p \equiv 5 \pmod 8$ and are able to prove that $p \equiv 5 \pmod {16}$ if $2p$ is a congruent number.
Comment: There is some problem in this calculation which I learned just now. I request you to withdraw thi
Comment: There is some problem in this calculation which I learned just now. I request you to withdraw thi
Externí odkaz:
http://arxiv.org/abs/2403.19685
Autor:
Ghosh, Arkabrata
The main aim of this article is to find all solutions of the Diophantine equation $x^2 + p^k=y^n$ where $p \equiv 1 \pmod 4$, $\frac{p-1}{3}$ is a perfect square and the class number of $\mathbb{Z}[\sqrt{-p}]$ is $2$. In this article, I used a method
Externí odkaz:
http://arxiv.org/abs/2402.19445
Autor:
Ghosh, Arkabrata
In this article, I study and solve the exponential Diophantine equation $M_p^{x} + (M_q + 1)^{y}= (lz)^2$ where $M_p$ and $M_q$ are Mersenne primes, $l$ is a prime number, and $x,y$, and $z$ are non-negative integers. Several illustrations are presen
Externí odkaz:
http://arxiv.org/abs/2307.07161
Autor:
Ghosh, Arkabrata, Zakharov, Dmitry
We calculate the volume of the tropical Prym variety of a harmonic double cover of metric graphs having non-trivial dilation. We show that the tropical Prym variety behaves discontinuously under deformations of the double cover that change the number
Externí odkaz:
http://arxiv.org/abs/2303.03904
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