Results 1 to 10 of about 983 (72)
Transactions of the London Mathematical Society, 2019 Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when ...
Harris B. Daniels +2 more
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Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves
Journal of Mathematical Cryptology, 2021 Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽p2, if an imaginary quadratic order O can be embedded in End(E) and a ...
Xiao Guanju, Luo Lixia, Deng Yingpu
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A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
Transactions of the London Mathematical Society, 2021 Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
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Elliptic curve and k-Fibonacci-like sequence
Scientific African, 2023 In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour +2 more
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MODULES OVER IWASAWA ALGEBRAS [PDF]
Journal of the Institute of Mathematics of Jussieu, 2001 Let $G$ be a compact $p$-valued $p$-adic Lie group, and let $\varLambda(G)$ be its Iwasawa algebra. The present paper establishes results about the structure theory of finitely generated torsion $\varLambda(G)$-modules, up to pseudo-isomorphism, which ...
J. Coates, P. Schneider, R. Sujatha
semanticscholar +1 more source
Bounded gaps between primes in Chebotarev sets [PDF]
Research in the Mathematical Sciences, 2014 A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes p1, p2 with |p1-p2| ≤ 600 as a consequence of the Bombieri-Vinogradov Theorem.
Jesse Thorner
semanticscholar +1 more source
Rank zero elliptic curves induced by rational Diophantine triples [PDF]
, 2020 Rational Diophantine triples, i.e. rationals a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares, are often used in construction of elliptic curves with high rank. In this paper, we consider the opposite problem and ask how small can be the
Dujella, Andrej, Mikić, Miljen
core +3 more sources
Weierstrass mock modular forms and elliptic curves [PDF]
, 2014 Mock modular forms, which give the theoretical framework for Ramanujan’s enigmatic mock theta functions, play many roles in mathematics. We study their role in the context of modular parameterizations of elliptic curves E/Q$E/\mathbb {Q}$.
Claudia Alfes +3 more
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Ramification in the division fields of elliptic curves with potential supersingular reduction
Research in Number Theory, 2016 Let d≥1 be fixed. Let F be a number field of degree d, and let E/F be an elliptic curve. Let E(F)tors be the torsion subgroup of E(F). In 1996, Merel proved the uniform boundedness conjecture, i.e., there is a constant B(d), which depends on d but not on
Álvaro Lozano‐Robledo
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Non‐vanishing theorems for central L‐values of some elliptic curves with complex multiplication
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1531-1578, December 2020., 2020 Abstract The paper uses Iwasawa theory at the prime p=2 to prove non‐vanishing theorems for the value at s=1 of the complex L‐series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K=Q(−q), where q is any prime ≡7mod8.
John Coates, Yongxiong Li
wiley +1 more source