and the Whittaker models of the inducing representation π M (cf. Theorem 2 of [4]). In this paper, Rodier’s theorem on the “heredity” of Whittaker models is extended to the non-algebraic setting of the n-fold metaplectic cover G̃ of G, where n is a positive integer such that F contains all of the n-th roots of unity. The main result is stated as a theorem in §2. In order to illustrate the situat...

We provide a clarification of scaling issues in simulation models, distinguishing between sample size determination, discovery of emergent properties involving a qualitative change in the behaviour of the system at an aggregate level, and ‘true’ scaling, the dependence of the quantitative behaviour of the system at any given level of aggregation, to its size. Scaling issues arise because we wan...

This is a summary of research which appears in a preprint of the same title. We prove a K-resolution theorem for simply connected CW-complexes K in extension theory in the class of metrizable compacta X. This means that if dimX ≤ K (in the sense of extension theory), n is the first element of N such that G = πn(K) 6= 0, and it is also true that πn+1(K) = 0, then there exists a metrizable compac...

Suppose π = (d1, d2, . . . , dn) and π = (d1, d ′ 2 , . . . , dn) are two positive nonincreasing degree sequences, write π ⊳ π if and only if π 6= π, ∑n i=1 di = ∑n i=1 d ′ i, and ∑j i=1 di ≤ ∑j i=1 di for all j = 1, 2, . . . , n. Let ρ(G) and μ(G) be the spectral radius and signless Laplacian spectral radius of G, respectively. Also let G and G be the extremal graphs with the maximal (signless...

We refine the definition of the fractional Galois ideal introduced in [Paul Buckingham. The canonical fractional Galois ideal at s = 0. J. Number Theory, 128(6):1749–1768, 2008] which was based on Snaith’s fractional ideal, allowing us to give a general relationship of this object with the Stark elements appearing in Rubin’s integral sharpening of Stark’s Conjecture. We motivate this by using a...

Let π = ⊗πv and π ′ = ⊗π ′ v be two irreducible, automorphic, cuspidal representations of GLm (AK). Using the logarithmic zero-free region of Rankin-Selberg L-function, Moreno established the analytic strong multi-plicity one theorem if at least one of them is self-contragredient, i.e. π and π ′ will be equal if they have finitely many same local components πv, π ′ v , for which the norm of pla...

Let π = ⊗πv and π ′ = ⊗π ′ v be two irreducible, automorphic, cuspidal representations of GLm (AK). Using the logarithmic zero-free region of Rankin-Selberg L-function, Moreno established the analytic strong multi-plicity one theorem if at least one of them is self-contragredient, i.e. π and π ′ will be equal if they have finitely many same local components πv, π ′ v , for which the norm of pla...

Let G be a finite group with given subgroups H and K. π an irreducible complex representation of such that its space H-invariant vectors as well the K-invariant are both one dimensional. vH (resp. vK) denote K-invariant) vector unit norm in G-invariant inner product 〈,〉π on π. Our interest is computing square absolute value 〈vH,vK〉π. This correlation constant c(π;H,K) defined by Gross [3]. In t...