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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-ph2017★ 12 cited
Poisson distribution for gaps between sums of two squares and level spacings for toral point scatterers
Tristan Freiberg, Pär Kurlberg, Lior Rosenzweig
We investigate the level spacing distribution for the quantum spectrum of the square billiard. Extending work of Connors--Keating, and Smilansky, we formulate an analog of the Hard…