Salem numbers and Pisot numbers via interlacing

We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the "obvious" limit points of the set of Salem numbers produced by our theorems, and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we show that all Salem numbers are produced via an interlacing construction.Comment: 21 pages, 5 figures, updated in response to reviewer comment

A tangled web of access to information: reflections on R (on the application of Evans) and another v Her Majesty's Attorney General

The Freedom of Information Act 2000 (‘FOIA’) came into force on 1 January 2005. It created, for the first time, a statutory right of access to information held by a wide range of public authorities. The right of access extends to all information held, regardless of how old the information is and the format in which it is held, unless one of the absolute exemptions listed in the Act is applicable, or the public interest test for disclosure is not satisfied in respect of a qualified exemption. Significantly, the Act also contains a power of ministerial veto, the effect of which is that orders to disclose information under the Act are rendered ineffective if a minister certifies that they have “reasonable grounds” for having formed the opinion that non-disclosure would not be unlawful. Prior to R (on the application of Evans) and another v Attorney General, there was a lack of certainty regarding what constituted ‘reasonable grounds’ for the issuance of a ministerial certificate. As well as clarifying the threshold for reasonable grounds for issuing a veto, this judgment also engages in a discussion of the relationship between three fundamental constitutional principles: the rule of law, separation of powers and parliamentary sovereignty to determine the extent to which it is legally and constitutionally legitimate for a court exercising powers of judicial review to strike down a Government Minister’s decision made under powers granted by Parliament to overturn an independent judicial tribunal’s judgment. Thus, the decision is of interest to those seeking to assess its potential contribution to discourse on common law constitutionalism