Modular forms of weight one and Galois representations

By J-P. Serre. 2003

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Class Field Towers (2010, background): “Serre [56], as well as Honda [25], Jehanne [531], in particular his thesis [532]).”
The subconvexity problem for Artin L–functions (2002, methodology): “For needed background on the theory of Artin L-functions we refer to [ Se ].”
SIEGEL MODULAR FORMS OF GENUS 2 ATTACHED TO ELLIPTIC CURVES (2006, unknown): “where the last group on the right is zero by a theorem of Tate ( [43]).”
POWERS OF THETA FUNCTIONS (2008, background): “MR 49 #8956 Zbl 0256.12001 [Serre 1977] J.-P. Serre, “Modular forms of weight one and Galois representations”, pp. 193–268 in Algebraic number fields: L-functions and Galois properties (Durham, 1975), Academic Press, London, 1977.”
On a theorem of Jordan (2003, background): “To go further, one needs a result of Tate (reproduced in [17], [12], [5]) which says that the field L has a quadratic extension L̃ having the following two properties: - L̃ is unramified over L (and hence also over Q( √ −283)); - L̃ is a Galois extension of Q.”
Shifted convolution sums and subconvexity bounds for automorphic L-functions (2004, unknown): “By Deligne’s proof [2] of the Ramanujan-Petersson conjecture for holomorphic cusp forms of integral weight k ≥ 2 (extended by Serre [24] to k = 1), we know that ∣∣a(m)∣∣ = ∣∣λf(m)∣∣ ≤ τ(m) (2.”