Pregled bibliografske jedinice broj: 1245760
Counting elliptic curves with prescribed level structures over number fields
Counting elliptic curves with prescribed level structures over number fields // Journal of the London Mathematical Society, 105 (2022), 4; 2415-2435 doi:10.1112/jlms.12564 (međunarodna recenzija, članak, znanstveni)
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Naslov
Counting elliptic curves with prescribed level
structures over number fields
Autori
Bruin, Peter ; Najman, Filip
Izvornik
Journal of the London Mathematical Society (0024-6107) 105
(2022), 4;
2415-2435
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
elliptic curves ; torsion
Sažetak
Harron and Snowden [11] counted the number of elliptic curves over Q up to height X with torsion group G for each possible torsion group G over Q. In this paper we generalize their result to all number fields and all level structures G such that the corresponding modular curve XG is a weighted projective line P(w0, w1) and the morphism XG → X(1) satisfies a certain condition. In particular, this includes all modular curves X1(m, n) with coarse moduli space of genus 0. We prove our results by defining a size function on P(w0, w1) following unpublished work of Deng [7], and working out how to count the number of points on P(w0, w1) up to size X.
Izvorni jezik
Engleski
POVEZANOST RADA
Projekti:
--KK.01.1.1.01.0004 - Provedba vrhunskih istraživanja u sklopu Znanstvenog centra izvrsnosti za kvantne i kompleksne sustave te reprezentacije Liejevih algebri (QuantiXLie) (Buljan, Hrvoje; Pandžić, Pavle) ( CroRIS)
HRZZ-IP-2018-01-1313 - Diofantska geometrija i primjene (DIOPHANT) (Kazalicki, Matija, HRZZ - 2018-01) ( CroRIS)
Profili:
Filip Najman
(autor)
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus