3,102 research outputs found
On ℓ-adic representations for a space of noncongruence cuspforms
No full textThis paper is concerned with a compatible family of 4-dimensional ℓ-adic representations ρℓ of GQ := Gal(Q/Q) attached to the space of weight-3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that:
1.
It is automorphic: the L-function L(s,ρℓ∨) agrees with the L-function for an automorphic form for GL4(AQ), where ρℓ∨ is the dual of ρℓ.
2.
For each prime p≥5 there is a basis hp = {hp+, hp-} of S3(Γ) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12.
The key point is that the representation ρℓ admits a quaternion multiplication structure in the sense of Atkin, Li, Liu, and Long
Compensation for Personal Injury in New Zealand - Its Rise and Fall
No full textThis article is a book review of Ian Campbell Compensation for Personal Injury in New Zealand: Its Rise and Fall (Auckland University Press, Auckland, 1996) 286 + x pages, $39.95. Atkin notes that New Zealand's accident compensation scheme was initially developed in a largely non-partisan way and was greeted positively. However, he notes that accident compensation has become a political football in recent years. Atkin thus recognises the timeliness of this book which provides the scheme's history and competing arguments for future change. Atkin concludes that the book's reference to the scheme's rise and fall is too pessimistic a picture, as the scheme continues to work well for many New Zealanders. However, Atkin notes that the book adds legitimate weight to the idea that accident compensation is under attack. Thus, with its grounding in the history of compensation mechanisms, the book is said to represent a valuable addition to the debate about future directions. 
The Drama of Reform: Theology and Theatricality, 1461–1553
No full textThis review considers The Drama of Reform by Tamara Atkin
Tort Law Text and Materials by Mark Lunney and Ken Oliphant
No full textThis article is a book review of Mark Lunney and Ken Oliphant, Tort Law Text and Materials Oxford University Press, Oxford, 2000, 819 + lix pages (Reg Retail NZ$95). Lunney and Oliphant's book is a book of materials and cases of English tort law developments, although the authors have both done research in New Zealand as well. Atkin reviews the tort law developments in England covered in the book and then compares it to that of New Zealand, including the torts of invasion of privacy and negligence. Atkin commends the book for its innovative writing and style. The frequent pattern of the book is to include critique and commentary after the relevant case law, which Atkin states are memorable and of high quality. 
Recommended from our members
[Photograph of Barbara Ann Atkin and Donna Lee Beaird]
No full textPhotograph of Miss Grand Prarie (Barbara Ann Atkin) and Miss Arlington (Donna Lee Beaird) holding a 30 inch pumpkin pie at the grand opening of Leonard's Arlington-Grand Prairie store
Jeffrey W. Cody, Nancy S. Steinhardt, Tony Atkin (ed.), Chinese Architecture and the Beaux-Arts, Honolulu : University of Hawai’i Press, 2011
No full textXie-Fouques Lingqiong. Jeffrey W. Cody, Nancy S. Steinhardt, Tony Atkin (ed.), Chinese Architecture and the Beaux-Arts, Honolulu : University of Hawai’i Press, 2011. In: Études chinoises, vol. 31, n°1,2012. pp. 165-169
Modular symbols over number fields
No full textLet K be a number field, R its ring of integers. For some classes of fields, spaces of cusp forms of weight 2 for GL(2;K) have been computed using methods based on modular symbols. J.E. Cremona [9] began the programme of extending the classical methods over Q to the case of imaginary quadratic fields. This work was continued by some of his Ph.D. students [35, 6, 22], and results have been obtained for some imaginary quadratic fields with small class number. More recently, P. Gunnells and D. Yasaki [18] have developed related algorithms for real quadratic fields.
The aim of this thesis is to contribute to the extension of the modular symbols method, when possible developing algorithms and implementations for effective computations. Some parts of the theory are purely algebraic and can be extended to all number fields. We generalise the theory for cusps and Manin symbols; we also describe a generalisation of Atkin-Lehner involutions and study other normaliser elements. On the other hand, all previous explicit computations for the imaginary quadratic field case were done only for specific fields. In the last part of this thesis we begin work towards a general implementation of the techniques used in this case. In particular, we are able to compute a fundamental domain of the hyperbolic 3-space for any imaginary quadratic field.
Implementations of the algorithms described in this thesis have been written by the author in the open-source mathematics software Sage [31]
Curves with many rational points via Atkin-Lehner involution
No full textIn this article, we use reductions of the Drinfeld modular curves X0(n) to obtain curves over finite fields Fq of a given genus with many Fq-rational points. The main idea is to divide the Drinfeld modular curves by an Atkin–Lehner involution, which has many fixed points to obtain a quotient with a better #{rational points}genus ratio. If we divide the Drinfeld modular curve X0(n) by an involution W, then the number of rational points of the quotient curve W\X0(n) is not less than half of the original number. On the other hand, if this involution has many fixed points, then by the Hurwitz genus formula, the genus of the curve W\X0(n) is much less than half of the g(X0(n))
Correction to: COVID-19 biomarkers for severity mapped to polycystic ovary syndrome
No full textFollowing publication of the original article, the
authors would like to correct the author group with
regards to the equal contributions: Stephen L. Atkin
and Alexandra E. Butler should be listed as joint senior
authors.
The author group has been updated above and the original article has been corrected
- …
