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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Towards a zero-one law for improvements to Dirichlet's approximation theorem
Dirichlet近似定理 改进 零一定律
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2023/5/10
In this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was...
Error term improvements for van der Corput transforms
Asymptotic analysis exponential sum trigonometric sum
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2012/5/9
We improve the error term in the van der Corput transform for exponential sums
\sum_{a \le n \le b} g(n) exp(2\pi i f(n)).
For many functions g and f, we can extract the next term in the asymptoti...
Improvements on Cantor-Zassenhaus Factorization Algorithm
Polynomial factorization Cantor-Zassenhaus
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2011/2/25
After revisiting Cantor-Zassenhaus polynomial factorization algorithm, we describe a new
simplified version of it, which requires less computational cost.
Asymptotics of coefficients of multivariate generating functions: improvements for multiple points
analytic combinatorics multivariate higher-order terms singularity analysis
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2010/12/14
Let F(x) = P 2Nd Fx be a multivariate power series with complex coefficients that converges in a neighborhood of the origin. Assume F = G/H for some functions G and H holomorphic in a neighborhood ...
Some improvements on the constants for the real Bohnenblust-Hille inequality
improvements constants real Bohnenblust-Hille inequality
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2010/12/6
A classical inequality due to Bohnenblust and Hille states that for every N ∈ N and every m-linear mapping U : ℓN 1 × · · · × ℓN 1 → C we have N X i1,...,im=1 U(ei1 , ..., eim) 2m m...
Improvements of Euler-Trapezoidal Type Inequalities with Higher-Order Convexity and Applications
Hadamard inequality Euler formula Convex functions Integral inequalities Numerical integration
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2008/7/1
We improve a bounds relating to Euler's formula for the case of a function with higher-order convexity properties. These are used to improve estimates of the error involved in the use of the trapezoid...