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On the average value of divisor sums in arithmetic progressions
(2005)
We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that "on average" these sums are close to the expected value. We also give applications of our result to sums ...
Values of the Euler Function in Various Sequences
(2005)
Let φ (n) and λ(n) denote the Euler and Carmichael functions, respectively. In this paper, we investigate the equation φ (n)r = λ(n)s, where r ≥ s ≥ 1 are fixed positive integers. We also study those positive integers n, ...
Efficient Statistical Mapping of Avian Count Data
(Environmental and Ecological Statistics, 2005)
We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of the Poisson model. The ...
On the Value Set of n! Modulo a Prime
(2005)
We show that for infinitely many prime numbers p there are at least log log p/ log log log p distinct residue classes modulo p that are not congruent to n! for any integer n.
Irrationality of Power Series for Various Number Theoretic Functions
(2005)
We study formal power series whose coefficients are taken to be a variety of number theoretic functions, such as the Euler, Möbius and divisor functions. We show that these power series are irrational over ℤ [X], and we ...
A Measure of Media Bias
(Department of Economics, 2005)
In this paper we estimate ADA (Americans for Democratic Action) scores for major media outlets such as the New York Times, USA Today, Fox News' Special Report, and all three network television news shows. Our estimates ...