Pith. sign in

REVIEW 4 cited by

The leading constant for rational points in families

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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

arxiv 2210.13559 v5 pith:C4GRGKKE submitted 2022-10-24 math.NT math.AG

Daniel Loughran , Nick Rome , Efthymios Sofos This is my paper · ORCID
classification math.NTmath.AG
keywords numberrationalasymptoticsconicsconjectureconstantcountingdiagonal
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We prove asymptotics for Serre's problem on the number of diagonal planar conics with a rational point and use this to put forward a new conjecture on counting the number of varieties in a family which are everywhere locally soluble.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Serre's problem for multiple conics

    math.NT 2025-04 conditional novelty 8.0 of 10

    For products of conic bundles over P^{n-1} with squarefree monomial coefficients, the count of soluble fibres matches the Loughran-Rome-Sofos asymptotic, and the Rédei symbol is equidistributed among admissible triples.

  2. An improved large sieve for quadratic characters via Hooley neutralisers and its applications

    math.NT 2025-06 conditional novelty 7.0 of 10

    Using Hooley neutralisers, a large sieve for quadratic characters is improved for multiplicatively weighted sequences, with applications to hyperbolic-region character sums.

  3. Rational points in a family of conics over $\mathbb{F}_2(t)$

    math.NT 2024-12 accept novelty 7.0 of 10

    Over F_2(t), the number of parameters y of height 2^M for which the conic x0^2+x0x1+yx1^2=t x2^2 has a rational point is asymptotically c 2^{2M}/M^{1/2}, with an explicit Euler product constant c.

  4. Solubility of a family of conics with polynomial coefficients in many variables

    math.NT 2025-11 reject novelty 6.0 of 10

    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.

Pith tools