Twisting of Siegel paramodular forms

Let $S_k(\Gamma^{\mathrm{para}}(N))$ be the space of Siegel paramodular forms of level $N$ and weight $k$. Let $p\nmid N$ and let $\chi$ be a nontrivial quadratic Dirichlet character mod $p$. Based on our previous work, we define a linear twisting map $\mathcal{T}_\chi:S_k(\Gamma^{\mathrm{para}}(N))\rightarrow S_k(\Gamma^{\mathrm{para}}(Np^4))$. We calculate an explicit expression for this twist and give the commutation relations of this map with the Hecke operators and Atkin-Lehner involution for primes $\ell\neq p$.Comment: 64 pages. In version 2, the paper has been shortened significantly and lengthy, technical proofs given in a separate appendix. In version 3, two typos are corrected. In version 4, we have included the full details of the proof of the local twisting theorem in the paper and improved the results with the L-function theore

Appendix to "Twisting of Siegel paramodular forms"

In this appendix we present an expanded version of Section 4 of our paper arXiv:1404.4596, including the proofs of all of the technical lemmas.Comment: 60 pages. In version 2, two typos have been corrected. The appendix has been incorporated into the main body of the paper and is therefore withdraw

Siegel modular forms of degree two attached to Hilbert modular forms

AbstractLet E/Q be a real quadratic field and π0 a cuspidal, irreducible, automorphic representation of GL(2,AE) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero Siegel paramodular newform F:H2→C with weight, level, Hecke eigenvalues, epsilon factor and L-function determined explicitly by π0. We tabulate these invariants in terms of those of π0 for every prime p of Q

On the equivariant and the non-equivariant main conjecture for imaginary quadratic fields

The Iwasawa main conjecture fields has been an important tool to study the arithmetic of special values of $L$-functions of Hecke characters of imaginary quadratic fields. To obtain the finest possible invariants it is important to know the main conjecture for all prime numbers $p$ and also to have an equivariant version at disposal. In this paper we first prove the main conjecture for imaginary quadratic fields for all prime numbers $p$, improving earlier results by Rubin. From this we deduce the equivariant main conjecture in the case that a certain $\mu$-invariant vanishes. For prime numbers $p\nmid 6$ which split in $K$, this is a theorem by a result of Gillard.Comment: 38 pages, completely revised version, inaccuracies and typos fixe

The importance of population differences: Influence of individual characteristics on the Australian public’s preferences for emergency care

A better understanding of the public’s preferences and what factors influence them is required if they are to be used to drive decision-making in health. This is particularly the case for service areas undergoing continual reform such as emergency and primary care. Accordingly, this study sought to determine if attitudes, socio-demographic characteristics and healthcare experiences influence the public’s intentions to access care and their preferences for hypothetical emergency care alternatives. A discrete choice experiment was used to elicit the preferences of Australian adults (n = 1529). Mixed logit regression analyses revealed the influence of a range of individual characteristics on preferences and service uptake choices across three different presenting scenarios. Age was associated with service uptake choices in all contexts, whilst the impact of other sociodemographics, health experience and attitudinal factors varied by context. The improvements in explanatory power observed from including these factors in the models highlight the need to further clarify their influence with larger populations and other presenting contexts, and to identify other determinants of preference heterogeneity. The results suggest social marketing programs undertaken as part of demand management efforts need to be better targeted if decision-makers are seeking to increase community acceptance of emerging service models and alternatives. Other implications for health policy, service planning and research, including for workforce planning and the possible introduction of a system of co-payments are discussed