3,701 research outputs found
Atkin, C C, 12316
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/369274Surname: ATKIN
Given Name(s) or Initials: C C
Military Service Number or Last Known Location: 12316
Missing, Wounded and Prisoner of War Enquiry Card Index Number: 47649179316
Item: [2016.0049.01601] "Atkin, C C, 12316
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
The Drama of Reform: Theology and Theatricality, 1461–1553
No full textThis review considers The Drama of Reform by Tamara Atkin
Implementing the Schoof-Elkies-Atkin Algorithm with NTL
No full textIn elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order of this subgroup. In particular, we often want to find a subgroup with large prime order. Hence when finding a suitable curve for cryptography, counting the number of points on the curve is an essential step in determining its security.
In 1985, René Schoof proposed the first deterministic polynomial-time algorithm for point counting on elliptic curves over finite fields. The algorithm was improved by Noam Elkies and Oliver Atkin, resulting in an algorithm which is sufficiently fast for practical purposes. The enhancements leveraged the arithmetic properties of the l-th classical modular polynomial, where l- is either an Elkies or Atkin prime. As the Match-Sort algorithm relating to Atkin primes runs in exponential time, it is eschewed in common practice.
In this thesis, I will discuss my implementation of the Schoof-Elkies-Atkin algorithm in C++, which makes use of the NTL package. The implementation also supports the computation of classical modular polynomials via isogeny volcanoes, based on the methods proposed recently by Bröker, Lauter and Sutherland.
Existing complexity analysis of the Schoof-Elkies-Atkin algorithm focuses on its asymptotic performance. As such, there is no estimate of the actual impact of the Match-Sort algorithm on the running time of the Schoof-Elkies-Atkin algorithm for elliptic curves defined over prime fields of cryptographic sizes. I will provide rudimentary estimates for the largest Elkies or Atkin prime used, and discuss the variants of the Schoof-Elkies-Atkin algorithm using their run-time performances.
The running times of the SEA variants supports the use Atkin primes for prime fields of sizes up to 256 bits. At this size, the selective use of Atkin primes runs in half the time of the Elkies-only variant on average. This suggests that Atkin primes should be used in point counting on elliptic curves of cryptographic sizes
Stability of domain walls in cylindrical layers of smectic C liquid crystals
No full textThe stability of the static domain wall reported by Atkin and Stewart for an infinite sample of concentric, cylindrical layers of smectic C liquid crystals arranged with a fixed inner radius a > 0 is considered. A criterion is derived as a test for stability. Various estimates on the relative magnitudes of the smectic elastic constants lead to physically meaningful stability results. The occurrence of such a wall indicates the relative magnitudes of the combinations of constants A12 ? A21 and A12 andplus; A21 andplus; 2A11 and, in a special case, can indicate when A12 andap; A21
Modular Forms on Noncongruence Subgroups and Atkin–Swinnerton-Dyer Relations
No full textWe give new examples of noncongruence subgroups T C SL2(Z) whose space of weight-3 cusp forms S3(Γ) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with respect to a weight-3 newform for a certain congruence subgroup. © A K Peters, Ltd
Broue-Enguehard maps and Atkin-Lehner involutions
No full textLet a be one of the ten integers such that the sum of their divisors divide 24. For each such e, (except 15) we give a map from an algebra of polynomial invariants of some finite group to the algebra of modular forms invariant under the Atkin-Lehner group of level e. These maps are motivated and inspired by constructions of modular lattices from self-dual codes over rings. This work generalizes Broue-Enguehard work in level one and three obtained from binary and ternary codes. (c) 2007 Elsevier Ltd. All rights reserved.X113sciescopu
Promoting Sexual Empowerment in Community-based Programmes
No full textHesperian is developing an action resource (book- and web-based tool) that will complement its widely used Where Women Have No Doctor and help community activists work more effectively on all the topics in that book, published originally in 1997. One issue the international team developing the new resource has prioritized is how to help community activists foster sexual empowerment for women. Lucille C. Atkin et al. describe the approach to sexuality in the book Taking Action (working title). Development (2009) 52, 114–117. doi:10.1057/dev.2008.81
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