Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields
Sign Up to like & getrecommendations! Published in 2018 at "Periodica Mathematica Hungarica"
DOI: 10.1007/s10998-018-0242-3
Abstract: In this paper we study the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields. For any such map we describe the cycle and the tree structures of the… read more here.
Keywords: elliptic curves; maps induced; induced endomorphisms; ordinary elliptic ... See more keywords
Frobenius distributions in short intervals for CM elliptic curves
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DOI: 10.1016/j.jnt.2018.01.007
Abstract: Abstract For an elliptic curve E / Q , Hasse's theorem asserts that # E ( F p ) = p + 1 − a p , where | a p | ≤ 2 p… read more here.
Keywords: frobenius distributions; elliptic curves; distributions short; short intervals ... See more keywords
Analogue of the Brauer–Siegel theorem for Legendre elliptic curves
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2018.05.006
Abstract: Abstract We prove an analogue of the Brauer–Siegel theorem for the Legendre elliptic curves over K = F q ( t ) . Namely, denoting by E d the elliptic curve with model y 2… read more here.
Keywords: analogue brauer; siegel theorem; elliptic curves; brauer siegel ... See more keywords
Supercharacters, elliptic curves, and the sixth moment of Kloosterman sums
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DOI: 10.1016/j.jnt.2019.01.004
Abstract: We connect the sixth power moment of Kloosterman sums to elliptic curves. This yields an elementary proof that $K_u$ with $p\nmid u$ are $O(p^{2/3})$. read more here.
Keywords: elliptic curves; kloosterman sums; moment kloosterman; supercharacters elliptic ... See more keywords
Typically bounding torsion on elliptic curves with rational j-invariant
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DOI: 10.1016/j.jnt.2021.10.003
Abstract: A family F of elliptic curves defined over number fields is said to be typically bounded in torsion if the torsion subgroups E(F )[tors] of those elliptic curves E/F ∈ F can be made uniformly… read more here.
Keywords: typically bounding; torsion; elliptic curves; bounding torsion ... See more keywords
Notes on anomalies, elliptic curves and the BS-D conjecture
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ab5ac3
Abstract: We consider anomaly cancellation for $SU(N)\times SU(2)\times U(1)$ gauge theories where the left-handed chiral multiplets are in higher $SU(2)$ representations. In particular, if the left-handed quarks and leptons transform under the triplet representation of $SU(2)$… read more here.
Keywords: anomalies elliptic; elliptic curves; curves conjecture; notes anomalies ... See more keywords
Cyclicity and exponents of CM elliptic curves modulo $p$ in short intervals
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DOI: 10.1090/tran/8197
Abstract: Let E be a CM elliptic curve defined over Q. We establish an asymptotic formula for the number of primes p for which the reduction modulo p of E is cyclic over short intervals. This… read more here.
Keywords: exponents elliptic; cyclicity exponents; elliptic curves; short intervals ... See more keywords
On the Refined Conjectures on Fitting Ideals of Selmer Groups of Elliptic Curves with Supersingular Reduction
Sign Up to like & getrecommendations! Published in 2019 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnz129
Abstract: In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ of an elliptic curve over $\mathbb{Q}$. Especially, we present a proof of the “weak main… read more here.
Keywords: elliptic curves; fitting ideals; selmer groups; reduction ... See more keywords
Constructions of LDPCs From Elliptic Curves Over Finite Fields
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DOI: 10.1109/lcomm.2017.2750660
Abstract: In this letter, a new framework for the construction of low density parity check codes is exposed. Parameters of the new codes are estimated, performance simulations are reported and compared with some classical constructions. read more here.
Keywords: finite fields; elliptic curves; ldpcs elliptic; constructions ldpcs ... See more keywords
Finding elliptic curves with a subgroup of prescribed size
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DOI: 10.1142/s1793042117500099
Abstract: Assuming the Generalized Riemann Hypothesis, we design a deterministic algorithm that, given a prime p and positive integer m = o(p1/2(logp)−4), outputs an elliptic curve E over the finite field ????p for which the cardinality… read more here.
Keywords: algorithm; subgroup prescribed; elliptic curves; finding elliptic ... See more keywords
HERON QUADRILATERALS VIA ELLIPTIC CURVES.
Sign Up to like & getrecommendations! Published in 2017 at "Rocky Mountain journal of mathematics"
DOI: 10.1216/rmj-2017-47-4-1227
Abstract: A Heron quadrilateral is a cyclic quadrilateral whose area and side lengths are rational. In this work, we establish a correspondence between Heron quadrilaterals and a family of elliptic curves of the form y 2… read more here.
Keywords: quadrilaterals via; via elliptic; elliptic curves; heron quadrilaterals ... See more keywords