Results 1 to 10 of about 12 (12)

Singular moduli of rth Roots of modular functions

Open Mathematics, 2023
When singular moduli of Hauptmodules generate ring class fields (resp. ray class fields) of imaginary quadratic fields, using the theory of Shimura reciprocity law, we determine a necessary and sufficient condition for singular moduli of rrth roots of ...
Choi SoYoung
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
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Ramanujan’s function k(τ)=r(τ)r2(2τ) and its modularity

Open Mathematics, 2020
We study the modularity of Ramanujan’s function k(τ)=r(τ)r2(2τ)k(\tau )=r(\tau ){r}^{2}(2\tau ), where r(τ)r(\tau ) is the Rogers-Ramanujan continued fraction.
Lee Yoonjin, Park Yoon Kyung
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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

Modular equations of a continued fraction of order six

Open Mathematics, 2019
We study a continued fraction X(τ) of order six by using the modular function theory. We first prove the modularity of X(τ), and then we obtain the modular equation of X(τ) of level n for any positive integer n; this includes the result of Vasuki et al ...
Lee Yoonjin, Park Yoon Kyung
doaj   +1 more source

On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

Open Mathematics, 2019
After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
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Capitulation of the 2-ideal classes of type (2, 2, 2) of some quartic cyclic number fields

Journal of Mathematical Cryptology, 2019
Let p≡3(mod4){p\equiv 3\pmod{4}} and l≡5(mod8){l\equiv 5\pmod{8}} be different primes such that pl=1{\frac{p}{l}=1} and 2p=pl4{\frac{2}{p}=\frac{p}{l}_{4}}. Put k=ℚ⁢(l){k=\mathbb{Q}(\sqrt{l})}, and denote by ϵ its fundamental unit. Set K=k⁢(-2⁢p⁢ϵ⁢l){K=k(
Azizi Abdelmalek, Jerrari Idriss, Zekhnini Abdelkader, Talbi Mohammed   +3 more
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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, Shin Dong Hwa, Yoon Dong Sung   +2 more
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Rigid meromorphic cocycles for orthogonal groups

Forum of Mathematics, Sigma
Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a p-adic analogue of Borcherds’ singular theta lift.
Lennart Gehrmann, Henri Darmon, Michael Lipnowski   +2 more
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Unit groups of some multiquadratic number fields and 2-class groups. [PDF]

Period Math Hung, 2022
Chems-Eddin MM.
europepmc   +1 more source