Kimball Martin
Published 2015-11-02Version 1
Many results are known regarding how much local information is required to determine a global object, such as a modular form, or a Galois or automorphic representation. We survey some things that are known and expected, and then explain recent joint work with Dinakar Ramakrishnan about comparing degree 2 Artin and automorphic representations which a priori may not correspond at certain infinite sets of places.
Comments: These are notes based on a talk I gave at the RIMS workshop, "Modular forms and automorphic representations," in February 2015; 14 pages
Non-existence of Ramanujan congruences in modular forms of level four
On pairs of p-adic L-functions for weight two modular forms
Congruence classes for modular forms over small sets
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