Results 1 to 10 of about 284 (57)
Orienting supersingular isogeny graphs
Journal of Mathematical Cryptology, 2020 We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
exaly +2 more sources
On a problem of Hasse and Ramachandra
Open Mathematics, 2019 Let K be an imaginary quadratic field, and let 𝔣 be a nontrivial integral ideal of K. Hasse and Ramachandra asked whether the ray class field of K modulo 𝔣 can be generated by a single value of the Weber function. We completely resolve this question when
Koo Ja Kyung +2 more
exaly +2 more sources
Class fields generated by coordinates of elliptic curves
Open Mathematics, 2022 Let KK be an imaginary quadratic field different from Q(−1){\mathbb{Q}}\left(\sqrt{-1}) and Q(−3){\mathbb{Q}}\left(\sqrt{-3}). For a nontrivial integral ideal m{\mathfrak{m}} of KK, let Km{K}_{{\mathfrak{m}}} be the ray class field modulo m{\mathfrak{m}}.
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
doaj +1 more source
Unitary Invertible Graphs of Finite Rings
Discussiones Mathematicae - General Algebra and Applications, 2021 Let R be a finite commutative ring with unity. In this paper, we consider set of additive and mutual additive inverses of group units of R and obtain interrelations between them.
Chalapathi Tekuri, Sajana Shaik
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CM liftings of $K3$ surfaces over finite fields and their applications to the Tate conjecture
Forum of Mathematics, Sigma, 2021 We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of $K3$ surfaces over finite fields.
Kazuhiro Ito +2 more
doaj +1 more source
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
doaj +1 more source
Pink's conjecture on unlikely intersections and families of semi-abelian varieties [PDF]
, 2020 The Poincar\'e torsor of a Shimura family of abelian varieties can be viewed both as a family of semi-abelian varieties and as a mixed Shimura variety.
Bertrand, Daniel, Edixhoven, Bas
core +3 more sources
On some extensions of Gauss’ work and applications
Open Mathematics, 2020 Let K be an imaginary quadratic field of discriminant dK{d}_{K} with ring of integers OK{{\mathcal{O}}}_{K}, and let τK{\tau }_{K} be an element of the complex upper half plane so that OK=[τK,1]{{\mathcal{O}}}_{K}={[}{\tau }_{K},1].
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
doaj +1 more source
Constructing elliptic curves of prime order [PDF]
, 2007 We present a very efficient algorithm to construct an elliptic curve E and a finite field F such that the order of the point group E(F) is a given prime number N.
Broker, Reinier, Stevenhagen, Peter
core +3 more sources
Matrices induced by arithmetic functions acting on certain Krein spaces
Special Matrices, 2017 In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
Cho Ilwoo
doaj +1 more source