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of 25
pro vyhledávání: '"Arul, Vishal"'
Autor:
Arul, Vishal, Müller, J. Steffen
We compute the rational points on the Atkin-Lehner quotient $X^+_0(125)$ using the quadratic Chabauty method. Our work completes the study of exceptional rational points on the curves $X^+_0(N)$ of genus between 2 and 6. Together with the work of sev
Externí odkaz:
http://arxiv.org/abs/2205.14744
Autor:
Arul, Vishal.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 113-116).
In this thesis, I study two problems in the ari
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 113-116).
In this thesis, I study two problems in the ari
Externí odkaz:
https://hdl.handle.net/1721.1/127911
Autor:
Adžaga, Nikola, Arul, Vishal, Beneish, Lea, Chen, Mingjie, Chidambaram, Shiva, Keller, Timo, Wen, Boya
We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus four, five, and six. We find that the
Externí odkaz:
http://arxiv.org/abs/2105.04811
Autor:
Arul, Vishal, Booher, Jeremy, Groen, Steven R., Howe, Everett W., Li, Wanlin, Matei, Vlad, Pries, Rachel, Springer, Caleb
We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C' are curves over a finite field K, with K-rational base points P and P', and let D and
Externí odkaz:
http://arxiv.org/abs/2102.11419
Autor:
Arul, Vishal
We classify all geometric torsion points on the Fermat quotients $y^n = x^d + 1$ where $n, d \ge 2$ are coprime. In addition, we classify all geometric torsion points on the generic superelliptic curve $y^n = (x - a_1) \cdots (x - a_d)$, extending a
Externí odkaz:
http://arxiv.org/abs/1910.14251
Autor:
Arul, Vishal
Fix distinct primes $\ell$ and $f$, a finite field $\mathbf{F}_{q}$ such that $q \equiv 1 \pmod{\ell f}$, and a character $\chi : \mathbf{F}_{q}^{\times} \to \mathbf{C}^{\times}$ of exact order $\ell f$. We present a new $\ell$-adic congruence for th
Externí odkaz:
http://arxiv.org/abs/1910.14249
Autor:
Arul, Vishal
In 2016, Yuri Zarhin gave formulas for "dividing a point on a hyperelliptic curve by 2." Given a point $P$ on a hyperelliptic curve $\mathcal{C}$, Zarhin gives the Mumford's representation of every degree $g$ divisor $D$ such that $2(D - g \infty) \s
Externí odkaz:
http://arxiv.org/abs/1810.07299
Publikováno v:
Open Book Series 2 (2019) 37-53
We describe an algorithm to compute the zeta function of a cyclic cover of the projective line over a finite field of characteristic $p$ that runs in time $p^{1/2 + o(1)}$. We confirm its practicality and effectiveness by reporting on the performance
Externí odkaz:
http://arxiv.org/abs/1806.02262
Autor:
ARUL, Vishal
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2021 Jan 01. 33(2), 607-625.
Externí odkaz:
https://www.jstor.org/stable/48618791
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