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Search: MSC category 11F46 ( Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms )

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1. CJM Online first

Mok, Chung Pang; Tan, Fucheng
Overconvergent Families of Siegel-Hilbert Modular Forms
We construct one-parameter families of overconvergent Siegel-Hilbert modular forms. This result has applications to construction of Galois representations for automorphic forms of non-cohomological weights.

Keywords:p-adic automorphic form, rigid analytic geometry
Categories:11F46, 14G22

2. CJM 2010 (vol 62 pp. 1060)

Darmon, Henri; Tian, Ye
Heegner Points over Towers of Kummer Extensions
Let $E$ be an elliptic curve, and let $L_n$ be the Kummer extension generated by a primitive $p^n$-th root of unity and a $p^n$-th root of $a$ for a fixed $a\in \mathbb{Q}^\times-\{\pm 1\}$. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of $E$ over $L_n$ in certain cases. The aim of this note is to explain how some of these predictions might be accounted for by Heegner points arising from a varying collection of Shimura curve parametrisations.

Categories:11G05, 11R23, 11F46

3. CJM 2009 (vol 61 pp. 395)

Moriyama, Tomonori
$L$-Functions for $\GSp(2)\times \GL(2)$: Archimedean Theory and Applications
Let $\Pi$ be a generic cuspidal automorphic representation of $\GSp(2)$ defined over a totally real algebraic number field $\gfk$ whose archimedean type is either a (limit of) large discrete series representation or a certain principal series representation. Through explicit computation of archimedean local zeta integrals, we prove the functional equation of tensor product $L$-functions $L(s,\Pi \times \sigma)$ for an arbitrary cuspidal automorphic representation $\sigma$ of $\GL(2)$. We also give an application to the spinor $L$-function of $\Pi$.

Categories:11F70, 11F41, 11F46

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