Results 11 to 20 of about 283 (48)

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
exaly   +2 more sources

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
doaj   +1 more source

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
doaj   +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

Counterexamples to a conjecture of Lemmermeyer [PDF]

, 1998
We produce infinitely many finite 2-groups that do not embed with index 2 in any group generated by involutions. This disproves a conjecture of Lemmermeyer and restricts the possible Galois groups of unramified 2-extensions, Galois over the rationals, of
Boston, Nigel, Leedham-Green, Charles
core   +1 more source

Stickelberger's congruences for absolute norms of relative discriminants [PDF]

, 2010
We give an improvement of a result of J. Martinet on Stickelberger's congruences for the absolute norms of relative discriminants of number fields, by using classical arguments of class field ...
Gras, Georges
core   +5 more sources

The Chevalley-Gras formula over global fields [PDF]

, 2020
In this article we give an adelic proof of the Chevalley-Gras formula for global fields, which itself is a generalization of the ambiguous class number formula. The idea is to reduce the formula to the Hasse norm theorem, the local and global reciprocity
Li, Jianing, Yu, Chia-Fu
core   +3 more sources

Representation fields for commutative orders [PDF]

, 2011
A representation field for a non-maximal order $\Ha$ in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of $\Ha$. Not every non-maximal order
Arenas-Carmona, Luis
core   +2 more sources

Curves, dynamical systems and weighted point counting [PDF]

, 2012
Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies that two such
Cornelissen, Gunther
core   +1 more source