Results 1 to 10 of about 284,852 (62)
Universal elliptic Gauß sums for Atkin primes in Schoof's algorithm [PDF]
arXiv, 2017 This work builds on earlier results. We define universal elliptic Gau{\ss} sums for Atkin primes in Schoof's algorithm for counting points on elliptic curves. Subsequently, we show these quantities admit an efficiently computable representation in terms of the $j$-invariant and two other modular functions.
Christian J. Berghoff
arxiv +5 more sources
Elliptic Gauß sums and Schoof's algorithm [PDF]
arXiv, 2016 We present a new approach to handling the case of Atkin primes in Schoof's algorithm for counting points on elliptic curves over finite fields. Our approach is based on the theory of polynomially cyclic algebras, which we recall as far as necessary. We then proceed to describe our method, which essentially relies on transferring costly computations in ...
Christian J. Berghoff
arxiv +6 more sources
Earth and Space Science, Volume 9, Issue 12, December 2022., 2022 Abstract Extreme precipitation events may cause flooding, slope failure, erosion, deposition, and damage to infrastructure over a regional scale, but the impacts of these events are often difficult to fully characterize. Regional‐scale landscape change occurred during an extreme rain event in June 2012 in northeastern Minnesota.
S. B. DeLong +7 more
wiley +1 more source
Simulation of the Deformation for Cycling Chemo-Mechanically Coupled Battery Active Particles with Mechanical Constraints [PDF]
Comput. Math. Appl. 149 (2023) 135-149, 2023 Next-generation lithium-ion batteries with silicon anodes have positive characteristics due to higher energy densities compared to state-of-the-art graphite anodes. However, the large volume expansion of silicon anodes can cause high mechanical stresses, especially if the battery active particle cannot expand freely.
arxiv +1 more source
Modeling and Simulation of Chemo-Elasto-Plastically Coupled Battery Active Particles [PDF]
Comput. Mech. (2024), 2023 As an anode material for lithium-ion batteries, amorphous silicon offers a significantly higher energy density than the graphite anodes currently used. Alloying reactions of lithium and silicon, however, induce large deformation and lead to volume changes up to 300%.
arxiv +1 more source
Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes [PDF]
Phys. Rev. B 93, 085102 (2016), 2015 The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in the warm dense matter regime, e.g. dense plasmas and laser excited solids. Also, the quality of density functional theory calculations crucially relies on the availability of accurate data for the exchange-correlation energy.
arxiv +1 more source
On the distribution of orders of Frobenius action on $\ell$-torsion of abelian surfaces [PDF]
, 2020 The computation of the order of Frobenius action on the $\ell$-torsion is a part of Schoof-Elkies-Atkin algorithm for point counting on an elliptic curve $E$ over a finite field $\mathbb{F}_q$. The idea of Schoof's algorithm is to compute the trace of Frobenius $t$ modulo primes $\ell$ and restore it by the Chinese remainder theorem.
arxiv +1 more source
On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average [PDF]
LMS J. Comput. Math. 18 (2015) 308-322, 2014 For an elliptic curve E/Q without complex multiplication we study the distribution of Atkin and Elkies primes l, on average, over all good reductions of E modulo primes p. We show that, under the Generalised Riemann Hypothesis, for almost all primes p there are enough small Elkies primes l to ensure that the Schoof-Elkies-Atkin point-counting algorithm
arxiv +1 more source
Limnology and Oceanography, EarlyView.Abstract Local and regional‐scaled studies point to the important role of lake type (natural lakes vs. reservoirs), surface water connectivity, and ecological context (multi‐scaled natural settings and human factors) in mediating lake responses to disturbances like drought.
Xinyu Sun +3 more
wiley +1 more source
Computing cardinalities of Q-curve reductions over finite fields [PDF]
LMS J. Comput. Math. 19 (2016) 115-129, 2016 We present a specialized point-counting algorithm for a class of elliptic curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generally, any elliptic curve over F\_{p^2} with a low-degree isogeny to its Galois conjugate curve. These curves have interesting cryptographic applications.
arxiv +1 more source