Abstract
The aim of this book is to give a gentle but complete introduction to the two interrelated theory of p-adic families of modular forms and of p-adic L-functions of modular forms. These theories and their generalizations to automorphic forms for group of higher ranks are now of fundamental importance in number theory. To our knowledge, this is the first textbook containing this material, which now is to be found scattered in many articles published during the last 40 years. Here we present a self-contained exposition of the theory leading to the construction of the eigencurves, and of the families of p-adic L-functions and adjoint p-adic L-functions on them.
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References
F. Diamond, J. Shurman, A First Course in Modular Forms. Graduate Texts in Mathematics, vol. 228 (Springer, New York, 2005)
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Bellaïche, J. (2021). Introduction. In: The Eigenbook. Pathways in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-77263-5_1
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DOI: https://doi.org/10.1007/978-3-030-77263-5_1
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-77262-8
Online ISBN: 978-3-030-77263-5
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