An element of an Adéle Group, sometimes called a Repartition in older literature. Adéles arise in both Number Fields and Function Fields. The adéles of a Number Field are the additive Subgroups of all elements in , where is the Place, whose Absolute Value is at all but finitely many s.

Let be a Function Field of algebraic functions of one variable. Then a Map which assigns to every Place of an element of such that there are only a finite number of Places for which .

**References**

Chevalley, C. C. *Introduction to the Theory of Algebraic Functions of One Variable.*
Providence, RI: Amer. Math. Soc., p. 25, 1951.

Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' *Not. Amer. Math. Soc.* **43**, 537-549, 1996.

© 1996-9

1999-05-25