Results 71 to 80 of about 699,908 (302)
Quadratic Twists of Elliptic Curves [PDF]
, 2011 [[abstract]]Let E be an elliptic curve defined over Q, and for each square-free rational integer d, let E_d denote the the quadratic twist of E by d (in brief, the d-twist). The question concerning the rank rk(Ed(Q)) of the Mordell-Weil group E_d(Q) (the
廖宏銘, Liao, Hung-Min
core
Average Analytic Ranks of Elliptic Curves over Number Fields
Forum of Mathematics, SigmaWe give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
doaj +1 more source
Advanced Engineering Materials, EarlyView.Postbuild annealing systematically modifies the phase fractions and morphology of EB‐PBF processed Mo–9Si–8B. Quantitative microstructure–property correlations reveal how controlled phase evolution enhances high‐temperature compressive strength and creep resistance.
Christopher Schmidt +5 more
wiley +1 more source
Faster Complete Addition Laws for Montgomery Curves
Transactions on Cryptographic Hardware and Embedded SystemsAn addition law for an elliptic curve is complete if it is defined for all possible pairs of input points on the elliptic curve. In Elliptic Curve Cryptography (ECC), a complete addition law provides a natural protection against side-channel attacks ...
Reza Rezaeian Farashahi +2 more
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Heuristics on pairing-friendly elliptic curves
Journal of Mathematical Cryptology, 2012 We present a heuristic asymptotic formula as for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree , with fixed discriminant, with rho-value bounded by a fixed such that , and with prime ...
Boxall John
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On Arithmetic Progressions on Elliptic Curves [PDF]
Experimental Mathematics, 1999 We study arithmetic progressions in the x-coordinates of rational points on elliptic curves. An infinite family of elliptic curves is found, each containing an arithmetic progression of length 8.
openaire +2 more sources
Advanced Engineering Materials, EarlyView.Deep‐UV (258 nm) femtosecond pulses enable uniform amorphous silicon writing on Si(100)/(111) with a six‐fold larger fluence amorphization window than NIR methods. Optimized fluence and overlap yield 20–45 nm uniform and continuous amorphous layers. Microscopy shows sharp interfaces, and real‐time reflectivity reveals nanosecond melt–resolidification ...
Wissal Benali +5 more
wiley +1 more source
Descent Via Isogeny on Elliptic Curves with Large Rational Torsion Subgroups. [PDF]
, 2008 We outline PARI programs which assist with various algorithms related to descent via isogeny on elliptic curves. We describe, in this context, variations of standard inequalities which aid the computation of members of the Tate-Shafarevich group.
Flynn, Eugene +7 more
core +1 more source
Efficient arithmetic on subfield elliptic curves over small finite fields of odd characteristic
Journal of Mathematical Cryptology, 2010 In elliptic curve cryptosystems, scalar multiplications performed on the curves have much effect on the efficiency of the schemes, and many efficient methods have been proposed. In particular, recoding methods of the scalars play an important role in the
Hakuta Keisuke +2 more
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Advanced Engineering Materials, EarlyView.This article investigates the dependence of the properties on the manufacturing orientation in the form of the inclination angle to the build plate of LPBF‐fabricated NiTi rods with a diameter of 150–220 µm. Metallographic, chemical, thermal, and mechanical characterization show behavior under identical manufacturing conditions that ranges from ...
Sandra Herzig +2 more
wiley +1 more source