Odd moments and adding fractions
Copyright policy )Odd moments and adding fractions
AbstractWe prove near‐optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an application, we prove near‐optimal upper bounds for the average of the refined singular series in the Hardy–Littlewood conjectures concerning the number of prime ‐tuples for odd. The main new ingredient is a near‐optimal upper bound for the number of solutions to when is odd, with and restrictions on the size of the numerators and denominators, which is of independent interest.
- Kuperberg, Vivian Zieve United States
- University of Manchester United Kingdom
- ETH Zurich Switzerland
- University of Manchester United Kingdom
- University of Manchester United Kingdom
Distribution of primes, Mathematics - Number Theory, FOS: Mathematics, Distribution of integers in special residue classes, Rational points, Number Theory (math.NT)
Distribution of primes, Mathematics - Number Theory, FOS: Mathematics, Distribution of integers in special residue classes, Rational points, Number Theory (math.NT)
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