REVIEW 2 cited by
Local solubility of a family of ternary conics over a biprojective base I
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
Let $f,g\in\mathbb{Z}[u_1,u_2]$ be binary quadratic forms. We provide upper bounds for the number of rational points $(u,v)\in\mathbb{P}^1(\mathbb{Q})\times\mathbb{P}^1(\mathbb{Q})$ such that the ternary conic \[ X_{(u,v)}: f(u_1,u_2)x^2 + g(v_1,v_2)y^2 = z^2 \] has a rational point. We also give some conditions under which lower bounds exist.
Forward citations
Cited by 2 Pith papers
-
Solubility of a family of conics with polynomial coefficients in many variables
An asymptotic for the density of soluble conics with polynomial coefficients is proposed, but the sign decomposition (6.5) that bridges the circle-method counts to the true count is false.
-
The density of elliptic curves over $\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny
Random Weierstrass equations over Z_p have Haar-measure densities for admitting a Q_p-rational 3-torsion point or 3-isogeny given by exact rational functions depending on p modulo 3.
Discussion (0). Continue with ORCID to comment.