The Continuum And Other Types of Serial Order. E. V Huntington. Second edition. 1955. 80 pp. 1 dollar. - Almost Periodic Functions. A. S. Besicovitch 1954. 180 pp. 1 dollar 75. - Treatise on ThermoDynamics. Max Planck (Translated by Alexander Ogg) Third Ed. 1955. 297 pp. 1 dollar 75. - Advanced Dynamics of a System of Rigid Bodies. E. J. Routh Sixth Ed. 1955. 484 pp. 1 dollar 95. - The Dynamical Theory of Gases. Sir James Jeans. Fourth Ed. Dover Publications, New York, 1955. 444 pp. 2 dollars.

1955 ◽  
Vol 59 (536) ◽  
pp. 574-574
Author(s):  
F. H. S.
Mathematika ◽  
1955 ◽  
Vol 2 (2) ◽  
pp. 128-131 ◽  
Author(s):  
J. D. Weston

2018 ◽  
Vol 14 (09) ◽  
pp. 2343-2368
Author(s):  
Giacomo Cherubini

We prove the existence of asymptotic moments and an estimate on the tails of the limiting distribution for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate on the asymptotic variance of the remainder that improves a result of Chamizo. Applying the results of the first part we prove the existence of limiting distribution and asymptotic moments for three functions that are integrated versions of the remainder, and were considered originally (with due adaptations to our settings) by Wolfe, Phillips and Rudnick, and Hill and Parnovski.


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