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On the norm of an idempotent Schur multiplier on the Schatten class
(American Mathematical Society, 2004)
We show that if the norm of an idempotent Schur multiplier on the Schatten class Sp lies sufficiently close to 1, then it is necessarily equal to 1. We also give a simple characterization of those idempotent Schur multipliers ...
Exponential Sums over Mersenne Numbers
(2004)
We give estimates for exponential sums of the form Σn≤N Λ(n) exp(2πiagn/m), where m is a positive integer, a and g are integers relatively prime to m, and Λ is the von Mangoldt function. In particular, our results yield ...
Significance of c /sqrt2 in relativistic physics
(American Institute of Physics, 2004)
In the description of relative motion in accelerated systems and gravitational fields, inertial and tidal accelerations must be taken into account, respectively. These involve a critical speed that in the first approximation ...
Almost All Palindromes Are Composite
(2004)
We study the distribution of palindromic numbers (with respect to a fixed base g ≥ 2) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes n ≤ x as x → ∞. Our results ...
Ultrarelativistic motion: inertial and tidal effects in Fermi coordinates
(Institute of Physics, 2004)
Fermi coordinates are the natural generalization of inertial Cartesian
coordinates to accelerated systems and gravitational fields. We study themotion
of ultrarelativistic particles and light rays in Fermi coordinates ...
Number Theoretic Designs for Directed Regular Graphs of Small Diameter
(Society for Industrial and Applied Mathematics, 2004)
In 1989, F. R. K. Chung gave a construction for certain directed h-regular graphs of small diameter. Her construction is based on finite fields, and the upper bound on the diameter
of these graphs is derived from bounds ...
Multiplicative Structure of Values of the Euler Function
(2004)
We establish upper bounds for the number of smooth values of the Euler function. In particular, although the Euler function has
a certain “smoothing” effect on its integer arguments, our results show that, in fact, most ...
Congruences and Exponential Sums with the Euler Function
(2004)
We give upper bounds for the number of solutions to congruences with the Euler function φ(n) and with the Carmichael function λ(n). We also give nontrivial bounds for certain exponential sums involving φ(n). Analogous ...
Dynamics of Relativistic Flows
(arXiv, 2004)
Dynamics of relativistic outflows along the rotation axis of a Kerr black hole is investigated using a simple model that takes into account the relativistic tidal force of the central source as well as the Lorentz force ...