title: Computing L-Invariants for the Symmetric Square of an Elliptic Curve

authors: Delbourgo, Daniel

subjects: Science & Technology

abstract: Let E be an elliptic curve over Q, and p≠2 a prime of good ordinary reduction. The p-adic L-function for Sym²E always vanishes at s = 1, even though the complex L-function does not have a zero there. The L-invariant itself appears on the right-hand side of the formula
ddsLp(Sym²E,s)∣∣∣s=1=Lp(Sym²E)×(1−α⁻²ᵖ)(1−pα⁻²ᵖ)×L∞(Sym²E,1)(2πi)⁻¹Ω+EΩ-E
where X²−aᵖ(E)X+p=(X−αᵖ)(X−βᵖ) with αp∈Z×ᵖ. We first devise a method to calculate Lp(Sym²E) effectively, then show it is non-trivial for all elliptic curves E of conductor NE≤300 with 4|NE, and almost all ordinary primes p < 17. Hence, in these cases at least, the order of the zero in Lp(Sym²E,s) at s = 1 is exactly one.

text: Computing L-Invariants for the Symmetric Square of an Elliptic Curve Let E be an elliptic curve over Q, and p≠2 a prime of good ordinary reduction. The p-adic L-function for Sym²E always vanishes at s = 1, even though the complex L-function does not have a zero there. The L-invariant itself appears on the right-hand side of the formula
ddsLp(Sym²E,s)∣∣∣s=1=Lp(Sym²E)×(1−α⁻²ᵖ)(1−pα⁻²ᵖ)×L∞(Sym²E,1)(2πi)⁻¹Ω+EΩ-E
where X²−aᵖ(E)X+p=(X−αᵖ)(X−βᵖ) with αp∈Z×ᵖ. We first devise a method to calculate Lp(Sym²E) effectively, then show it is non-trivial for all elliptic curves E of conductor NE≤300 with 4|NE, and almost all ordinary primes p < 17. Hence, in these cases at least, the order of the zero in Lp(Sym²E,s) at s = 1 is exactly one.

year: 2019

title: Wonder and empathy in environmental ethics

authors: van Zyl, Liezl

abstract: My aim in this article to argue that wonder is a basic moral capacity, akin to the capacity for empathy, that is required for the virtue of environmental benevolence. I begin by examining Geoffrey Frasz’s account of benevolence as a set of environmental virtues, and I identify a gap that not only threatens the coherence of Frasz’s theory, but also points to an important cause of our widespread apathy toward the environment: the inherently limited and biased nature of the capacity for empathy. My proposal is that the capacity for wonder can fill this gap, that is, I think wonder can play the role in environmental benevolence that empathy plays in interpersonal benevolence.

text: Wonder and empathy in environmental ethics My aim in this article to argue that wonder is a basic moral capacity, akin to the capacity for empathy, that is required for the virtue of environmental benevolence. I begin by examining Geoffrey Frasz’s account of benevolence as a set of environmental virtues, and I identify a gap that not only threatens the coherence of Frasz’s theory, but also points to an important cause of our widespread apathy toward the environment: the inherently limited and biased nature of the capacity for empathy. My proposal is that the capacity for wonder can fill this gap, that is, I think wonder can play the role in environmental benevolence that empathy plays in interpersonal benevolence.

year: 2025

title: Research and development absorptive capacity: a Māori perspective

authors: Ruckstuhl, Katharina

subjects: computer science

abstract: This paper presents a view of research and development absorptive capacity from a Māori perspective. The assessment is part of a case study of a longitudinal programme – Science for Technological Innovation: Kia kotahi mai – Te Ao Putaiao me te Ao Hanagarau that aims to increase Aotearoa New Zealand’s capacity to use sci-tech for economic benefit. The paper finds that while Aotearoa New Zealand’s macro policy and meso institutional levels have become more responsive to Māori research and development demands, at the micro level of the individual or the firm there are still constraints given the small numbers of Māori in science, technology, engineering and mathematics. In response to this, a novel model of Māori sci-tech capacity is under development that considers not only research and development technical capacities, but also the human and relational capacities required to accelerate absorptive capacity to respond to Māori social and economic aspirations.

text: Research and development absorptive capacity: a Māori perspective This paper presents a view of research and development absorptive capacity from a Māori perspective. The assessment is part of a case study of a longitudinal programme – Science for Technological Innovation: Kia kotahi mai – Te Ao Putaiao me te Ao Hanagarau that aims to increase Aotearoa New Zealand’s capacity to use sci-tech for economic benefit. The paper finds that while Aotearoa New Zealand’s macro policy and meso institutional levels have become more responsive to Māori research and development demands, at the micro level of the individual or the firm there are still constraints given the small numbers of Māori in science, technology, engineering and mathematics. In response to this, a novel model of Māori sci-tech capacity is under development that considers not only research and development technical capacities, but also the human and relational capacities required to accelerate absorptive capacity to respond to Māori social and economic aspirations.

year: 2019