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Carlitz exponential : ウィキペディア英語版
Carlitz exponential
In mathematics, the Carlitz exponential is a characteristic ''p'' analogue to the usual exponential function studied in real and complex analysis. It is used in the definition of the Carlitz module – an example of a Drinfeld module.
==Definition==

We work over the polynomial ring F''q''() of one variable over a finite field F''q'' with ''q'' elements. The completion C of an algebraic closure of the field F''q''((''T''−1)) of formal Laurent series in ''T''−1 will be useful. It is a complete and algebraically closed field.
First we need analogues to the factorials, which appear in the definition of the usual exponential function. For ''i'' > 0 we define
:() := T^ - T, \,
:D_i := \prod_ ()^^\infty \frac.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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