The variance of the number of prime polynomials in short intervals and in residue classes

By Jon P Keating, Z. Rudnick. 2012

84 citations recorded by the source corpus.

We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial ingredient in our work are recent equidistribution results of N. Katz.

Subfields: Algebra and Number Theory, Artificial Intelligence, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b71281ff44db55849857a7f86ac0670972b30f61

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Jon P Keating
2. Z. Rudnick
3. L. Bary‐Soroker
4. Kannan Soundararajan
5. Julio Andrade
6. M. Young
7. Alexandra Florea
8. Peter Sarnak

In Artificial Intelligence

1. Z. Rudnick
2. Jon P Keating

In Geometry and Topology

1. Jon P Keating
2. Z. Rudnick
3. L. Bary‐Soroker
4. Julio Andrade

Citations in the corpus

• Squarefree polynomials and Mobius values in short intervals and arithmetic progressions (2015, methodology): “Note that multiplicativity (and the “weak multiplicativity” condition) excludes the case of the von Mangoldt function, treated in [20] where we are counting prime polynomials in short intervals or arithmetic progressions.”
• PRIME POLYNOMIALS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS (2013, background): “In what follows we show how to derive an almost everywhere convergence, including small m, from a result of Keating and Rudnick [9].”