This introductory chapter sets out the book's focus, namely equidistribution results over larger and larger finite extensions of a given finite field. Emanuel Kowalski drew attention to the interest of having equidistribution results over, for example, prime fields 𝔽p, that become better and better as p grows. This question is addressed in Chapter 28, where the problem is to make effective the estimates, already given in the equicharacteristic setting of larger and larger extensions of a given finite field. Chapter 29 points out some open questions about “the situation over ℤ” and gives some illustrative examples. The chapter concludes by pointing out two potential ambiguities of notation.
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