Matthew Emerton is a mathematician working in number theory whose work connects modular forms, representation theory and arithmetic geometry. His authored account of classical modular forms as automorphic forms gives a precise translation between a weight- holomorphic function on the upper half-plane and an arithmetically invariant function on an adelic group.[ref]
The translation converts a transformation rule into invariance and differentiation conditions. In particular, being holomorphic becomes annihilation by a suitable differential operator, while the weight becomes a character under rotations. This places classical modular forms in the same representation-theoretic language as more general smooth automorphic forms. His author page provides the note and identifies his research area as number theory.[ref]
https://www.math.uchicago.edu/~emerton/. Author homepage and Miscellaneous Notes
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Matthew Emerton may refer to various individuals, but there aren’t any widely recognized figures by that name up to my last knowledge update in October 2023. If you have more specific information or context, such as a particular field (e.g., science, sports, arts), I might be able to provide more accurate information. Please clarify!