Ping Ngai Chung

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We give a general framework for uniform, constant-time oneand two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by projecting to the xline or Kummer surface, where we can exploit faster and more uniform pseudomultiplication, before recovering the proper “signed” output back on the curve or(More)
We give oneand two-dimensional scalar multiplication algorithms for Jacobians of genus 2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudomultiplication, before recovering the proper “signed” output back on the Jacobian. This extends the work of López and Dahab, Okeya and Sakurai, and Brier and Joye to(More)
We prove that an isoperimetric region in R2 with density er must be convex and contain the origin, and provide numerical evidence that circles about the origin are isoperimetric, as predicted by the Log-Convex Density Conjecture. Acknowledgements: We thank our advisor Frank Morgan for his patience and invaluable input. We also thank Diana Davis, Sean Howe(More)
In their breakthrough paper in 2006, Goldston, Graham, Pintz, and Yıldırım 1 proved several results about bounded gaps between products of two distinct primes. Frank 2 Thorne expanded on this result, proving bounded gaps in the set of square-free numbers with 3 r prime factors for any r ≥ 2, all of which are in a given set of primes. His results yield 4(More)
The prime number theorem is one of the most fundamental theorems of analytic number theory, stating that the prime counting function, π(x), is asymptotic to x/ log x. However, it says little about the parity of π(n) as an arithmetic function. Using Selberg’s sieve, we prove a positive lower bound for the proportion of positive integers n such that π(n) is r(More)
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