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Convolution and EquidistributionSato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)$
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Nicholas M. Katz

Print publication date: 2012

Print ISBN-13: 9780691153308

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153308.001.0001

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The Situation over ℤ: Results

The Situation over ℤ: Results

(p.173) Chapter 28 The Situation over ℤ: Results
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter treats an integer monic polynomial f(x) ɛ ℤ[x] of degree n ≤ 2 which, over ℂ, is “weakly supermorse,” meaning that it has n distinct roots in ℂ, its derivative f'(x) has n − 1 distinct roots (the critical points) α‎ᵢ ɛ ℂ, and the n − 1 values f(α‎ᵢ) (the critical values) are all distinct in ℂ.

Keywords:   number theory, interger monic polynomials, supermorse

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