Results 21 to 30 of about 284 (50)

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
doaj   +1 more source

Large Cyclic Subgroups of Jacobians of Hyperelliptic Curves [PDF]

, 2007
In this paper we obtain conditions on the divisors of the group order of the Jacobian of a hyperelliptic genus 2 curve, generated by the complex multiplication method described by Weng (2003) and Gaudry (2005). Examples, where these conditions imply that
Ravnshoj, Christian Robenhagen
core   +3 more sources

Ray class invariants over imaginary quadratic fields

, 2011
Let $K$ be an imaginary quadratic field of discriminant less than or equal to -7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater than 1.
Jung, Ho Yun, Koo, Ja Kyung, Shin, Dong Hwa   +2 more
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Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
doaj   +1 more source

On Colmez's product formula for periods of CM-abelian varieties

, 2012
Colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field K, analogous to the standard product formula in algebraic number theory.
Obus, Andrew
core   +1 more source

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
doaj   +1 more source

The Galois theory of the lemniscate [PDF]

, 2012
This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by proving the irreducibility of lemnatomic polynomials, which are analogs of ...
Cox, David A., Hyde, Trevor
core  

Varieties of sums of powers and moduli spaces of (1,7)-polarized abelian surfaces

, 2017
We study the geometry of some varieties of sums of powers related to the Klein quartic. This allows us to describe the birational geometry of certain moduli spaces of abelian surfaces.
Bolognesi, Michele, Massarenti, Alex
core   +2 more sources

CM relations in fibered powers of elliptic families

, 2017
Let $E_\lambda$ be the Legendre family of elliptic curves. Given $n$ linearly independent points $P_1,\dots , P_n \in E_\lambda\left(\overline{\mathbb{Q}(\lambda)}\right)$ we prove that there are at most finitely many complex numbers $\lambda_0$ such ...
André, Bombieri, David, Fabrizio Barroero, Ford, Habegger, Lang, Masser, Pila, Silverman, Zannier   +10 more
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Complex Hyperbolic Surfaces of Abelian Type [PDF]

, 2004
2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ...
Holzapfel, R.
core