Eisenstein Series , Crystals , and Ice

  title={Eisenstein Series , Crystals , and Ice},
  author={Benjamin Brubaker and Daniel Bump and Solomon Friedberg},
Automorphic forms are generalizations of periodic functions; they are functions on a group that are invariant under a discrete subgroup. A natural way to arrange this invariance is by averaging. Eisenstein series are an important class of functions obtained in this way. It is possible to give explicit formulas for their Fourier coefficients. Such formulas can provide clues to deep connections with other fields. As an example, Langlands’ study of Eisenstein series inspired his far-reaching… CONTINUE READING
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