In this paper we study matrices A = (aij) whose (i, j) -entry is a function of i/j; that is, aij = f(i/j) for some f : Q → C. We obtain a formula for the truncated determinants in the case where f is multiplicative, linking them to determinants of truncated Toeplitz matrices. We apply our formula to obtain several determinants of number-theoretic matrices. Mathematics Subject Classification 200...

Abstract An approach to find the field equation solution of the Randall-Sundrum model with the S/Z2 extra axis is presented. We closely examine the infrared singularity. The vacuum is set by the 5 dimensional Higgs field. Both the domain-wall and the anti-domain-wall naturally appear, at the ends of the extra compact axis, by taking a new infrared regularization. The stability is guaranteed fro...

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called ‘multi-harmonic’ periodogram, which is being used for detection of non-sinusoidal signals, and is based on the least-squares fitting of truncated Fourier series. The recent investigation (Baluev 2008) made for the LombScargle periodogram is extended to the more general multi-har...

We consider the problem of determining a pair of functions (u, f) satisfying the heat equation ut−∆u = φ(t)f(x, y), where (x, y) ∈ Ω = (0, 1)× (0, 1) and the function φ is given. The problem is ill-posed. Under a slight condition on φ, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier se...

We report on a computation of congruent numbers, which subject to the Birch and Swinnerton-Dyer conjecture is an accurate list up to 10. The computation involves multiplying large theta series as per Tunnell (1983). The first method, which we describe in some detail, uses a multimodular disk based technique for multiplying polynomials out-of-core which minimises expensive disk access by keeping...