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pro vyhledávání: '"Genao, Tyler"'
Autor:
Bourdon, Abbey, Genao, Tyler
In 1996, Merel showed there exists a function $B\colon \mathbb{Z}^+\rightarrow \mathbb{Z}^+$ such that for any elliptic curve $E/F$ defined over a number field of degree $d$, one has the torsion group bound $\# E(F)[\textrm{tors}]\leq B(d)$. Based on
Externí odkaz:
http://arxiv.org/abs/2409.08214
Autor:
Genao, Tyler
We analyze the fields of definition of cyclic isogenies on elliptic curves to prove the following uniformity result: for any number field $F_0$ which satisfies an isogeny condition, there exists a constant $B:=B(F_0)\in\mathbb{Z}^+$ such that for any
Externí odkaz:
http://arxiv.org/abs/2405.05507
Autor:
Genao, Tyler
Publikováno v:
Ramanujan J. 63 (2024), no. 2, 409--429
Given a number field $F_0$ that contains no Hilbert class field of any imaginary quadratic field, we show that under GRH there exists an effectively computable constant $B:=B(F_0)\in\mathbb{Z}^+$ for which the following holds: for any finite extensio
Externí odkaz:
http://arxiv.org/abs/2210.16977
Autor:
Genao, Tyler
We show there exist polynomial bounds on torsion of elliptic curves which come from a fixed geometric isogeny class. More precisely, for an elliptic curve $E_0$ defined over a number field $F_0$, for each $\epsilon>0$ there exist constants $c_\epsilo
Externí odkaz:
http://arxiv.org/abs/2210.10177
Autor:
Genao, Tyler
We prove that the family $\mathcal{I}_{F_0}$ of elliptic curves over number fields that are geometrically isogenous to an elliptic curve with $F_0$-rational $j$-invariant is typically bounded in torsion. Under an additional uniformity assumption, we
Externí odkaz:
http://arxiv.org/abs/2112.11566
Autor:
Akande, A. P., Genao, Tyler, Haag, Summer, Hendon, Maurice D., Pulagam, Neelima, Schneider, Robert, Sills, Andrew V.
Publikováno v:
Journal of the Ramanujan Mathematical Society 38 (2023) 121--128
Following Cayley, MacMahon, and Sylvester, define a non-unitary partition to be an integer partition with no part equal to one, and let $\nu(n)$ denote the number of non-unitary partitions of size $n$. In a 2021 paper, the sixth author proved a formu
Externí odkaz:
http://arxiv.org/abs/2112.03264
Autor:
Genao, Tyler
A family $\mathcal{F}$ of elliptic curves defined over number fields is said to be typically bounded in torsion if the torsion subgroups $E(F)[$tors$]$ of those elliptic curves $E_{/F}\in \mathcal{F}$ can be made uniformly bounded after removing from
Externí odkaz:
http://arxiv.org/abs/2102.10417
Autor:
Genao, Tyler
Publikováno v:
In Journal of Number Theory September 2022 238:823-841
Publikováno v:
In Expositiones Mathematicae December 2021 39(4):604-623
Publikováno v:
Acta Arith. 175 (2016), no. 1, 71-100
Define the sequence $\{b_n\}$ by $b_0=1,b_1=1, b_2=2,b_3=1$, and $$b_n=\begin{cases} \frac{b_{n-1}b_{n-3}-b_{n-2}^2}{b_{n-4}}&\textrm{if}~ n\not\equiv 0\pmod 3, \frac{b_{n-1}b_{n-3}-3b_{n-2}^2}{b_{n-4}}&\textrm{if}~ n\equiv 0\pmod 3. We relate this s
Externí odkaz:
http://arxiv.org/abs/1508.02464