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Ordinary p -adic Eisenstein series and p -adic L -functions for unitary groups

Ming-Lun Hsieh (2011)

Annales de l’institut Fourier

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for GL 2 × 𝒦 × by the method of Eisenstein congruence on G U ( 3 , 1 ) , where 𝒦 is an imaginary quadratic field. We construct a p -adic family of ordinary Eisenstein series on the group of unitary similitudes G U ( 3 , 1 ) with the optimal constant term which is basically the product of the Kubota-Leopodlt p -adic L -function and a p -adic L -function for GL 2 × 𝒦 × . This construction also provides a different point of view of p -adic...

p -adic ordinary Hecke algebras for GL ( 2 )

Haruzo Hida (1994)

Annales de l'institut Fourier

We study the p -adic nearly ordinary Hecke algebra for cohomological modular forms on G L ( 2 ) over an arbitrary number field F . We prove the control theorem and the independence of the Hecke algebra from the weight. Thus the Hecke algebra is finite over the Iwasawa algebra of the maximal split torus and behaves well under specialization with respect to weight and p -power level. This shows the existence and the uniqueness of the (nearly ordinary) p -adic analytic family of cohomological Hecke eigenforms...

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