Results 11 to 20 of about 36,762 (203)
The Frobenius twists of elliptic curves over global function fields
, 2023 25 pages, 0 ...
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On the Mertens Conjecture for Function Fields [PDF]
, 2013 We study an analogue of the Mertens conjecture in the setting of global function fields. Building on the work of Cha, we show that most hyperelliptic curves do not satisfy the Mertens conjecture, but that if we modify the Mertens conjecture to have a ...
Humphries, Peter
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Notes on the Parity Conjecture
, 2012 This is an expository article, based on a lecture course given at CRM Barcelona in December 2009. The purpose of these notes is to prove, in a reasonably self-contained way, that finiteness of the Tate-Shafarevich group implies the parity conjecture for ...
Dokchitser, Tim
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Tetrahedral Elliptic Curves and the local-global principle for Isogenies
, 2014 We study the failure of a local-global principle for the existence of $l$-isogenies for elliptic curves over number fields $K$. Sutherland has shown that over $\mathbb{Q}$ there is just one failure, which occurs for $l=7$ and a unique $j$-invariant, and ...
Banwait, Barinder Singh, Cremona, John
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, 2022 Fix a prime number $p$. Let $\mathbb{F}_q$ be a finite field of characteristic coprime to 2, 3, and $p$, which also contains the primitive $p$-th root of unity $μ_p$. Based on the works by Swinnerton-Dyer and Klagsbrun, Mazur, and Rubin, we prove that the probability distribution of the sizes of prime Selmer groups over a family of cyclic prime twists ...
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Torsion points on elliptic curves over a global field
Manuscripta Mathematica, 1979 Let C be an elliptic curve defined over a global field K and denote by CK the group of rational points of C over K. The classical Nagell-Lutz-Cassels theorem states, in the case of an algebraic number field K as groud field, a necessary condition for a point in CK to be a torsion point, i.e. a point of finite order.
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Advanced Engineering Materials, EarlyView.The wettability of aluminum droplets (Al) on different copper substrates (Cu), where liquid Al spreads on solid Cu surfaces to form a liquid–solid interface, is studied numerically and experimentally. The experimental and numerical results show good agreement in the fast‐spreading regime.
Shan Lyu +8 more
wiley +1 more source
, 2003 A telegraphic survey of some of the standard results and conjectures about the set $C({\bf Q})$ of rational points on a smooth projective absolutely connected curve $C$ over ${\bf Q}$.Comment: 6 ...
Dalawat, Chandan Singh
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On a BSD-type formula for L-values of Artin twists of elliptic curves [PDF]
, 2020 This is an investigation into the possible existence and consequences of a Birch-Swinnerton-Dyer-type formula for L-functions of elliptic curves twisted by Artin representations.
Dokchitser, Vladimir +2 more
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Advanced Engineering Materials, EarlyView.This study demonstrates how optimizing laser power, scanning speed, and hatching distance in laser powder bed fusion can boost the productivity of Inconel 718 manufacturing by up to 29% while maintaining mechanical integrity. The work delivers a validated process window and cost–time analysis, offering industry‐ready guidelines for efficient additive ...
Amir Behjat +7 more
wiley +1 more source