Beurling zeta functions, generalised primes, and fractal membranes

We study generalised prime systems P (1 < p(1) <= p(2) <= ..., with p(j) is an element of R tending to infinity) and the associated Beurling zeta function zeta p(s) = Pi(infinity)(j=1)(1 - p(j)(-s))(-1). Under appropriate assumptions, we establish various analytic properties of zeta p(s), including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of zeta p(s). Further we study 'well-behaved' g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on N-2. Some of the above results are relevant to the second author's theory of 'fractal membranes', whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.

Intellectual property management in M&A transactions

Purpose – The purpose of this paper is to focus on the intellectual property (IP) aspects of mergers and acquisitions (M&A) transactions. Design/methodology/approach – A holistic approach is proposed that embraces IP as an integral part of the M&A process in the form of a roadmap for the strategic and purposeful management of IP assets in M&A deals. Findings – Addressing IP issues in transactions in isolation can lead to undesirable consequences (e.g. considerable costs for unplanned purchases of rights). IP due diligence and IP integration project processes can be automated using collaborative software solutions. Thereby, risk can be reduced through the creation of a high level of transparency and predefined responsibilities. Practical implications – Although the proposed IP management framework is based on intellectual property matters relevant to German jurisdiction, conclusions derived and the proposed roadmap are transferable to other jurisdictions and hence have a broader relevance. Evidence for this is provided by the successful application of the roadmap in the context of the multinational transaction stated above. Originality/value – This paper is based on the authors' collective experience, insight and reflected observation of M&A practice gained in advisory M&A roles in management consultancies over a period of more than a decade. The paper summarizes the authors' reflections and observations and brings these into the context of the current management literature. Moreover, this paper builds on earlier published research.