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1. CJM Online first
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)
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)
$L$-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 |