Elliptic Curves, Modular Forms and Iwasawa Theory [electronic resource] : In Honour of John H. Coates' 70th Birthday, Cambridge, UK, March 2015 / edited by David Loeffler, Sarah Livia Zerbes.

1. A.Berti, M.Bertolini, R.Venerucci: Congruences between modular forms and the Birch and Swinnerton-Dyer conjecture -- 2. T.Bouganis: P-adic measures for Hermitian modular forms and the Rankin–Selberg method -- 3. A.Conti, A.Iovita, J.Tilouine: Big image of Galois representations associated with finite slope p-adic families of modular forms -- 4. A.Dabrowski: Behaviour of the order of Tate–Shafarevich groups for the quadratic twists of X0(49) -- 5. T.Fukaya, K.Kato, R.Sharifi: Compactifications of S-arithmetic quotients for the projective general linear group -- 6. R.Greenberg: On the structure of Selmer groups -- 7. H.Hida: Control of Lambda-adic Mordell-Weil groups -- 8. M.Kakde: Some congruences for non-CM elliptic curves -- 9. M.Kim: Diophantine geometry and non-abelian reciprocity laws I -- 10. G.Kings: On p-adic interpolation of motivic Eisenstein classes -- 11. T. Lawson, C.Wuthrich: Vanishing of some Galois cohomology groups for elliptic curves -- 12. P.Schneider, O.Venjakob: Coates–Wiles homomorphisms and Iwasawa cohomology for Lubin–Tate extensions -- 13. A.Wiles, A.Snowden: Big image in compatible systems.

Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields. .