Results 1 to 10 of about 43 (43)

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

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, Tetsushi Ito, Teruhisa Koshikawa   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms

Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 33-48, December 2020., 2020
Abstract We define twisted Eisenstein series Es±(h,k;τ) for s∈C, and show how their associated period functions, initially defined on the upper half complex plane H, have analytic continuation to all of C′:=C∖R⩽0. We also use this result, as well as properties of various zeta functions, to show that certain cotangent‐zeta sums behave like quantum ...
Amanda Folsom
wiley   +1 more source

On class groups of random number fields

Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 927-953, October 2020., 2020
Abstract The main aim of this paper is to disprove the Cohen–Lenstra–Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probability weights appearing in the general form of the heuristics.
Alex Bartel, Hendrik W. Lenstra Jr.
wiley   +1 more source

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

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

Groups of generalized G‐type and applications to torsion subgroups of rational elliptic curves over infinite extensions of Q

Transactions of the London Mathematical Society, Volume 6, Issue 1, Page 22-52, December 2019., 2019
Abstract 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 changing base to the compositum of all number fields with Galois group G.
Harris B. Daniels, Maarten Derickx, Jeffrey Hatley   +2 more
wiley   +1 more source