5 citations · 15 across the 9 of their papers we have counts for
9 papers
On Elliptic Sequences over Commutative Rings
Junyan Xu
We define elliptic sequences over a commutative ring as sequences indexed by the (positive) integers satisfying a 4-parameter, highly symmetric family of homogeneous quartic relati…
An Elementary Formal Proof of the Group Law on Weierstrass Elliptic Curves in any Characteristic
David Kurniadi Angdinata, Junyan Xu
Elliptic curves are fundamental objects in number theory and algebraic geometry, whose points over a field form an abelian group under a geometric addition law. Any elliptic curve…
On cyclic strong exceptional collections of line bundles on surfaces
Alexey Elagin, Junyan Xu, Shizhuo Zhang
We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation i…
Fusible numbers and Peano Arithmetic
Jeff Erickson, Gabriel Nivasch, Junyan Xu
Inspired by a mathematical riddle involving fuses, we define the "fusible numbers" as follows: is fusible, and whenever are fusible with , the number …
Burgess bounds for short character sums evaluated at forms II: the mixed case
Lillian B. Pierce
This work proves a Burgess bound for short mixed character sums in dimensions. The non-principal multiplicative character of prime conductor may be evaluated at any "admiss…
Burgess bounds for short character sums evaluated at forms
Lillian B. Pierce, Junyan Xu
In this work we establish a Burgess bound for short multiplicative character sums in arbitrary dimensions, in which the character is evaluated at a homogeneous form that belongs to…