Iwasawa Theory 2012 pp 401-441 | Cite as

# Nearly Overconvergent Modular Forms

## Abstract

We introduce and study finite slope nearly overconvergent (elliptic) modular forms. We give an application of this notion to the construction of the Rankin-Selberg *p*-adic L-function on the product of two eigencurves..

## Keywords

Modular Form Irreducible Component Eisenstein Series Admissible Pair Fredholm Determinant## Notes

### Acknowledgements

The author would like to thank Giovanni Rosso and Chris Skinner for interesting conversations during the preparation of this work and Vincent Pilloni for pointing out an error in a previous version of this text. He would like also to thank Pierre Colmez who encouraged him to write this note. He is also grateful to the organizers of the conference Iwasawa 2012 held in Heidelberg for their invitation and for giving the opportunity to publish this paper in the proceedings of this conference. This work was also lectured during the Postech winter school in January 2013. The author would like to thank the organizers of this workshop for their invitation. Finally the author would like to thank the Florence Gould Foundation for its support when he was a Member at the Institute for Advanced Studies and when some part of this work was conceived.

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