On the topological aspects of arithmetic elliptic curves
Kazuma Morita

TL;DR
This paper constructs a topological family encompassing all elliptic curves over Q, offering geometric insights into their Hasse-Weil L-functions, especially for those with Mordell-Weil rank ≤ 1.
Contribution
It introduces a novel topological framework that includes all elliptic curves over Q and connects this to geometric interpretations of their L-functions.
Findings
Provides a topological family containing all elliptic curves over Q
Offers geometric interpretations of Hasse-Weil L-functions for rank ≤ 1
Establishes a new perspective linking topology and elliptic curve L-functions
Abstract
In this short note, we shall construct a certain topological family which contains all elliptic curves over Q and, as an application, show that this family provides some geometric interpretations of the Hasse-Weil L-function of an elliptic curve over Q whose Mordell-Weil group is of rank .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Polynomial and algebraic computation
