Zobrazeno 1 - 10
of 202
pro vyhledávání: '"RAY, ANWESH"'
Autor:
Ray, Anwesh
Let $n$ be a cubefree natural number and $p\geq 5$ be a prime number. Assume that $n$ is not expressible as a sum of the form $x^3+y^3$, where $x,y\in \mathbb{Q}$. In this note, we study the solutions (or lack thereof) to the equation $n=x^3+y^3$, wh
Externí odkaz:
http://arxiv.org/abs/2409.17921
Autor:
Müller, Katharina, Ray, Anwesh
Let $E_{/\mathbb{Q}}$ be an elliptic curve and $p$ an odd prime such that $E$ has good ordinary reduction at $p$ and the Galois representation on $E[p]$ is irreducible. Then Greenberg's $\mu=0$ conjecture predicts that the Selmer group of $E$ over th
Externí odkaz:
http://arxiv.org/abs/2409.15056
Autor:
Nguyen, Khoa D., Ray, Anwesh
We explore distribution questions for rational maps on the projective line $\mathbb{P}^1$ over $\mathbb{Q}$ within the framework of arithmetic dynamics, drawing analogies to elliptic curves. Specifically, we investigate counting problems for rational
Externí odkaz:
http://arxiv.org/abs/2408.15648
Autor:
Ray, Anwesh
This article advances the results of Duke on the average surjectivity of Galois representations for elliptic curves to the context of Drinfeld modules over function fields. Let $F$ be the rational function field over a finite field. I establish that
Externí odkaz:
http://arxiv.org/abs/2407.14264
Autor:
Ray, Anwesh, Shingavekar, Pratiksha
Let $p \in \{3, 5\}$ and consider a cyclic $p$-extension $L/\mathbb{Q}$. We show that there exists an effective positive density of elliptic curves $ E $ defined over $ \mathbb{Q} $, ordered by height, that are diophantine stable in $ L $.
Comme
Comme
Externí odkaz:
http://arxiv.org/abs/2406.12561
Autor:
Ray, Anwesh
Let $\mathbb{F}_q$ be the finite field with $q$ elements, $F:=\mathbb{F}_q(T)$ and $F^{\operatorname{sep}}$ a separable closure of $F$. Set $A$ to denote the polynomial ring $\mathbb{F}_q[T]$. Let $\mathfrak{p}$ be a non-zero prime ideal of $A$, and
Externí odkaz:
http://arxiv.org/abs/2406.05524
Autor:
Müller, Katharina, Ray, Anwesh
Via a novel application of Iwasawa theory, we study Hilbert's tenth problem for number fields occurring in $\mathbb{Z}_p$-towers of imaginary quadratic fields $K$. For a odd prime $p$, the lines $(a,b) \in \mathbb{P}^1(\mathbb{Z}_p)$ are identified w
Externí odkaz:
http://arxiv.org/abs/2406.01443
Autor:
Ghosh, Sohan, Ray, Anwesh
Publikováno v:
Research in the Mathematical Sciences Vol 12, No. 2 (2025)
This paper explores Iwasawa theory from a graph theoretic perspective, focusing on the algebraic and combinatorial properties of Cayley graphs. Using representation theory, we analyze Iwasawa-theoretic invariants within $\mathbb{Z}_\ell$-towers of Ca
Externí odkaz:
http://arxiv.org/abs/2405.04361
Autor:
Ray, Anwesh
Given a prime $p\geq 5$, a conjecture of Greenberg predicts that the $\mu$-invariant of the $p$-primary Selmer group should vanish for most elliptic curves with good ordinary reduction at $p$. In support of this conjecture, I show that the $5$-primar
Externí odkaz:
http://arxiv.org/abs/2404.09009
Autor:
Ray, Anwesh, Shingavekar, Pratiksha
Let $a$ be an integer which is not of the form $n^2$ or $-3 n^2$ for $n\in \mathbb{Z}$. Let $E_a$ be the elliptic curve with rational $3$-isogeny defined by $E_a:y^2=x^3+a$, and $K:=\mathbb{Q}(\mu_3)$. Assume that the $3$-Selmer group of $E_a$ over $
Externí odkaz:
http://arxiv.org/abs/2403.18034