Should one generalize the Weyl calculus to an adelic setting ?
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As indicated by the question mark, this chapter is a tentative one. One of its purposes is to point towards one reason for doing pseudo-differential analysis in an adelic setting, beyond the obvious observation that dealing with prime numbers one at a time, when possible, certainly clarifies things. On the other hand, one can also find some reasons not to do so, especially if one restricts one’s interest, as will be the case here, to adeles of the field Q.
KeywordsZeta Function Wigner Function Eisenstein Series Homogeneous Component Symbolic Calculus
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