Results 171 to 180 of about 4,610 (199)
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A supersingularity criterion of elliptic curves
Journal of Mathematical Sciences, 1997A well-known Belyi theorem states that an arbitrary algebraic curve defined over \(\overline \mathbb{Q}\) can be mapped onto the projective line \(\mathbb{P}^1\) so that the whole of ramification will be concentrated over three points of \(\mathbb{P}^1\) (we may assume that these points are \(\infty, 0,1)\).
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On the Iwasawa $\mu $-invariants of supersingular elliptic curves
Acta Arithmetica, 2020This paper considers elliptic curves \(E\) and certain torsion Iwasawa modules attached to \(E\) and a fixed odd prime \(p\). Let \(X(E)\) be the dual of the \(p\)-Selmer group of \(E\) over the \(p\)-cyclotomic extension \(\mathbb Q_\infty/\mathbb Q\). In previous work with \textit{R. Barman} [Bull. Braz. Math. Soc. (N.S.) 41, No.
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Supersingular Elliptic Curves in Cryptography
2007I will survey the checkered history of supersingular elliptic curves in cryptography, from their first consideration in the seminal papers of Koblitz and Miller, to their rejection after the discovery of the Weil and Tate pairing attacks on the discrete logarithm problem for these curves, and concluding with their resurrection alongside the discovery ...
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On the supersingular reduction of elliptic curves
Proceedings of the Indian Academy of Sciences - Section A, 1987Let E be an elliptic curve over \({\mathbb{Q}}\), and let p be a prime of supersingular reduction for E. The author shows that the 2-complement of \(E({\mathbb{F}}_ p)\) is cyclic. In particular, if \(E_ a\) is the curve \(y^ 2=(x^ 2+1)(x+a)\) (a\(\in {\mathbb{Q}})\) the author combines the above result with Elkies' theorem (that there are infinitely ...
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Iwasawa theory for elliptic curves at supersingular primes
Inventiones Mathematicae, 2003Let \(p\) be an odd prime, \({\mathbb Q}_{\infty} = \bigcup_{n}\;F_{n}\) the cyclotomic \({\mathbb Z}_{p}\)-extension of \({\mathbb Q},\) \(\wedge\) the usual Iwasawa algebra. In the Iwasawa theory of elliptic curves at good ordinary primes, the Main Conjecture states that the Selmer group over \({\mathbb Q}_{\infty}\) is \(\wedge\)-cotorsion and the ...
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Understanding and Calibration of Charge Storage Mechanism in Cyclic Voltammetry Curves
Angewandte Chemie - International Edition, 2021Xiangjun Pu, Dong Zhao, Zhongxue Chen
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A kilonova following a long-duration gamma-ray burst at 350 Mpc
Nature, 2022Jillian Rastinejad +2 more
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