Shenxing Zhang

activity

20122026

most cited

ℓ

-Class groups of fields in Kummer towers

10 citations · 11 across the 13 of their papers we have counts for

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10 papers · 1 filter

math.NT2023

On a comparison of Cassels pairings of different elliptic curves

Shenxing Zhang

Let $e_{1}, e_{2}, e_{3}$ be nonzero integers satisfying $e_{1} + e_{2} + e_{3} = 0$ . Let $(a, b, c)$ be a primitive triple of odd integers satisfying $e_{1} a^{2} + e_{2} b^{2} + e_{3} c^{2} = 0$ . Denote by $E: y^2=x(x-e_1…

math.NT2023

On the quadratic twist of elliptic curves with full $2$ -torsion

Zhangjie Wang, Shenxing Zhang

Let $E : y^{2} = x (x - a^{2}) (x + b^{2})$ be an elliptic curve with full $2$ -torsion group, where $a$ and $b$ are coprime integers and $2 (a^{2} + b^{2})$ is a square. Assume that the $2$ -Selmer group…

math.NT2021

On non-congruent numbers with $8 a \pm 1$ type odd prime factors and tame kernels

Shenxing Zhang

Let $n$ be a positive square-free integer, where every odd prime factor of $n$ has form $8 a \pm 1$ . We determine when $n$ is non-congruent with second minimal $2$ -primary Shafarevic…

math.NT2021

On the Newton polygons of twisted $L$ -functions of binomials

Shenxing Zhang

Let $χ$ be an order $c$ multiplicative character of a finite field and $f (x) = x^{d} + λ x^{e}$ a binomial with $(d, e) = 1$ . We study the twisted classical and $T$ -adic Newton polygons of $f$ …

math.NT2020

The virtual periods of linear recurrence sequences in cyclotomic fields

Shenxing Zhang

A linear recurrence sequence in a cyclotomic field produces a sequence of the generating fields of each term. We show that the later sequence is periodic after removing the first f…

math.NT2020

The $3$ -class groups of $Q (3 p)$ and its normal closure

Jianing Li, Shenxing Zhang

We determine the $3$ -class groups of $Q (3 p)$ and $K = Q (3 p, - 3)$ when $p \equiv 4, 7 mod 9$ is a prime and $3$ is a cubic modulo $p$ . This co…

math.NT2019★ 10 cited

$ℓ$ -Class groups of fields in Kummer towers

Jianing Li, Yi Ouyang, Yue Xu +1

Let $ℓ$ and $p$ be prime numbers and $K_{n, m} = Q (p^{\frac{1}{ℓ ^{n}}}, ζ_{2 ℓ^{m}})$ . We study the $ℓ$ -class group of $K_{n, m}$ in this paper. When $ℓ = 2$ , we dete…

math.NT2015

Newton polygons of $L$ -functions of polynomials $x^{d} + a x^{d - 1}$ with $p \equiv - 1 mod d$

Yi Ouyang, Shenxing Zhang

For prime $p \equiv - 1 mod d$ and $q$ a power of $p$ , we obtain the slopes of the $q$ -adic Newton polygons of $L$ -functions of $x^{d} + a x^{d - 1} \in F_{q} [x]$ with respect to fini…

math.NT2012★ 1 cited

On non-congruent numbers with 3 modulo 8 prime factors

Shenxing Zhang

In this paper, we will give a series of non-congruent numbers with $\equiv 3 (mod 8)$ prime factors.

math.NT2012

On non-congruent numbers with 1 modulo 4 prime factors

Yi Ouyang, Shenxing Zhang

In this paper, we use the 2-decent method to find a series of odd non-congruent numbers $\equiv 1 (mod 8)$ whose prime factors are $\equiv 1 (mod 4)$ such that the congruent elliptic cu…

On a comparison of Cassels pairings of different elliptic curves

On the quadratic twist of elliptic curves with full 2-torsion

On non-congruent numbers with 8a±1 type odd prime factors and tame kernels

On the Newton polygons of twisted L-functions of binomials

The virtual periods of linear recurrence sequences in cyclotomic fields

The 3-class groups of Q(3p​) and its normal closure

ℓ-Class groups of fields in Kummer towers

Newton polygons of L-functions of polynomials xd+axd−1 with p≡−1modd

On non-congruent numbers with 3 modulo 8 prime factors

On non-congruent numbers with 1 modulo 4 prime factors

On the quadratic twist of elliptic curves with full $2$ -torsion

On non-congruent numbers with $8 a \pm 1$ type odd prime factors and tame kernels

On the Newton polygons of twisted $L$ -functions of binomials

The $3$ -class groups of $Q (3 p)$ and its normal closure

$ℓ$ -Class groups of fields in Kummer towers

Newton polygons of $L$ -functions of polynomials $x^{d} + a x^{d - 1}$ with $p \equiv - 1 mod d$