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The variance of the number of prime polynomials in short intervals and in residue classes
variance the number of prime polynomials short intervals residue classes Number Theory
2012/4/23
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 i...
Random multiplicative functions in short intervals
Random multiplicative functions short intervals
2010/11/24
We consider random multiplicative functions taking the values $\pm 1$. Using Stein's method for normal approximation, we prove a central limit theorem for the sum of such multiplicative functions in a...
Assume the Riemann Hypothesis. For every ǫ > 0 we show that there is a constant C(ǫ) such that for all large x, the interval [x, x + C(ǫ)px] contains an integer all of whose prime facto...
On the Symmetry of Square-Free Supported Arithmetical Functions in Short Intervals
Symmetry Square-free short intervals
2008/6/27
On the Symmetry of Square-Free Supported Arithmetical Functions in Short Intervals.
On the Fourth Power Mean of the Character Sums Over Short Intervals
character sums short intervals fourth power mean asymptotic formula
2007/12/11
The main purpose of this paper is to study the mean value properties of the character sums over the interval $\left[1, \frac{p}{8}\right)$ by using the mean value theorems of the Dirichlet L-functions...