The variance of the number of prime polynomials in short intervals and in residue classes (Q2878686)
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scientific article; zbMATH DE number 6340331
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The variance of the number of prime polynomials in short intervals and in residue classes |
scientific article; zbMATH DE number 6340331 |
Statements
5 September 2014
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distribution of primes
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function field
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unitarized Frobenius matrix
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The variance of the number of prime polynomials in short intervals and in residue classes (English)
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The authors resolve function field analogs of conjectures on the variance of the number of prime numbers: (1) in short intervals, and (2) in arithmetic sequences. A careful analysis brings the proof of these analogs to rest upon results of \textit{N. M. Katz} [Convolution and equidistribution. Sato-Tate theorems for finite-field Mellin transforms. Princeton, NJ: Princeton University Press (2012; Zbl 1261.11084)] for the equidistribution (as the field order \(q \to \infty\)) of the unitarized Frobenius matrices of the respectively appropriate type of Dirichlet character.
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