This paper provides evidence on organizational structure, geographic diversification, and performance at bank holding companies (BHCs). First, we show that a BHC's member banks benefit from access to the parent organization's ...

Is entrepreneurship an innate ability or an acquired skill? Can entrepreneurial acumen be achieved and enhanced through education and training, or are certain people “born” to be entrepreneurs or to act entrepreneurially? ...

It is shown that the Fourier-Whittaker coefficients of Eisenstein series on the n-fold cover of GL(n) are L-functions, improving prior results of T. Suzuki.

We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ...

We establish upper bounds for multiplicative character sums and exponential sums over sets of integers that are described by various properties of their digits in a fixed base g ≥ 2. Our main tools are the Weil and ...

For an m × n matrix A with nonnegative real entries, Atkinson, Moran and Watterson proved the inequality s(A)3 ≤ mns(AAtA), where At is the transpose of A, and s(·) is the sum of the entries. We extend this result to finite ...

An RSA modulus is a product M = pl of two primes p and l. We show that for almost all RSA moduli M, the number of sparse exponents e (which allow for fast RSA encryption) with the property that gcd(e,φ(M)) = 1 (hence RSA ...

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 ...

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 ...

Notice that 1_2_3_4+1 = 52 , 2_3_4_5+1 = 112 , 3_4_5_6+1 = 192 , . . . . Indeed, it is well known that the product of any four consecutive integers always differs by one from a perfect square. However, a little experimentation ...

In this paper we present a decoupling inequality that shows that multivariate U-statistics can be studied as sums of (conditionally) independent random variables. This result has important implications in several areas of ...

In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of Hp spaces for 0 < p < ∞. In this paper, we show that their method extends to higher dimensions ...

The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear k-correlations of n > k independent random variables.

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, ...

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the ...

We present a spectral mapping theorem for semigroups on any Banach space E. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for E-valued functions. This characterization ...

The spectrum of the kinematic dynamo operator for an ideally conducting fluid and the spectrum of the corresponding group acting in the space of continuous divergence free vector fields on a compact Riemannian manifold ...

We give necessary and sufficient conditions for the Hardy operator to be bounded on a rearrangement invariant quasi-Banach space in terms of its Boyd indices.

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A0,A1) such that A0 and A1 are isometric to X⊕V, and any intermediate space obtained using ...

There is increasing interest in predicting ecological processes. Methods to accomplish such predictions must account for uncertainties in observation, sampling, models, and parameters. Statistical methods for spatio-temporal ...