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math.NT2017
Sparser variance for primes in arithmetic progression
Roger Baker, Tristan Freiberg
We obtain an analog of the Montgomery-Hooley asymptotic formula for the variance of the number of primes in arithmetic progressions. In the present paper the moduli are restricted…
math.NT2017
Fractional parts of polynomials over the primes. II
Roger Baker
We consider the distance to the nearest integer of f(p), where f is a quadratic polynomial with irrational leading coefficient. This distance is very small as a function of p, for…