We show that using character sum estimates due to H. Iwaniec leads to an improvement of recent results about the distribution and finding RSA moduli M = pl, where p and l are primes, with prescribed bit patterns. We are now able to specify about n bits instead of about n/2 bits as in the previous work. We also show that the same result of H. Iwaniec can be used to obtain an unconditional versio...

1 Riemann integration 2 1.1 Partitions and Riemann sums . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 A criterion for integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Upper and Lower Riemann Sums . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 The refinement of a partition . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Properties of upper an...

A two-dimensional Riemann solver is proposed for the solution of hyperbolic systems of conservation laws in two dimensions of space. The solver approximates the solution of a so-called angular two-dimensional Riemann problem as the weighted sum of the solutions of one-dimensional Riemann problems. The weights are proportional to the aperture of the regions of constant state. The two-dimensional...

In this paper, we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military b...

We study the problem of factoring univariate polynomials over finite fields. Under the assumption of the Extended Riemann Hypothesis (ERH), Gao [Gao01] designed a polynomial time algorithm that fails to factor only if the input polynomial satisfies a strong symmetry property, namely square balance. In this paper, we propose an extension of Gao’s algorithm that fails only under an even stronger ...

Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, i...

Let [Formula: see text] be the argument of Riemann zeta-function at point text]. For and define its antiderivatives as where is a specific constant depending on In 1925, Littlewood proved, under Hypothesis (RH), that for 1946, Selberg unconditionally established explicit asymptotic formulas second moments This was extended by Fujii text], when Assuming RH, we give formula moment up to second-or...

This article deals with the regulation of water 6ow in open-channels modelled by Saint-Venant equations. By means of a Riemann invariants approach, we deduce stabilizing control laws for a single horizontal reach without friction. The stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies. A control law design base...

A hyperplane arrangement is said to satisfy the “Riemann hypothesis” if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley for certain families of arrangements which are defined for any irreducible root system and was proved for the root system An−1. The proof is based on an explicit formula [1, 2, 11] for the characteristi...