Stationary phase analysis of generalized cubic phase mask wavefront coding

2013 ◽  
Vol 298-299 ◽  
pp. 67-74 ◽  
Author(s):  
Ming Liu ◽  
Liquan Dong ◽  
Yuejin Zhao ◽  
Mei Hui ◽  
Wei Jia
Keyword(s):  
Stationary Phase ◽  
Phase Analysis ◽  
Phase Mask ◽  
Cubic Phase ◽  
Wavefront Coding ◽  
Stationary Phase Analysis

A new subconvex bound for GL(3) L-functions in the t-aspect

2020 ◽  
pp. 1-28
Author(s):  
Keshav Aggarwal
Keyword(s):  
Stationary Phase ◽  
Phase Analysis ◽  
Stationary Phase Analysis

We revisit Munshi’s proof of the [Formula: see text]-aspect subconvex bound for [Formula: see text] [Formula: see text]-functions, and we are able to remove the “conductor lowering” trick. This simplification along with a more careful stationary phase analysis allows us to improve Munshi’s bound to [Formula: see text]

Analysis of wavefront coding imaging with cubic phase mask decenter and tilt

2016 ◽  
Vol 55 (25) ◽  
pp. 7009 ◽  
Author(s):  
Yijian Wu ◽  
Liquan Dong ◽  
Yuejin Zhao ◽  
Ming Liu ◽  
Xuhong Chu ◽  
...  
Keyword(s):  
Phase Mask ◽  
Cubic Phase ◽  
Wavefront Coding

scholarly journals Sub-Weyl subconvexity for Dirichlet -functions to prime power moduli

2015 ◽  
Vol 152 (4) ◽  
pp. 825-875 ◽  
Author(s):  
Djordje Milićević
Keyword(s):  
Stationary Phase ◽  
Phase Analysis ◽  
Wide Class ◽  
Prime Power ◽  
Exponential Sums ◽  
New Method ◽  
Central Value ◽  
Stationary Phase Analysis

We prove a subconvexity bound for the central value $L(\frac{1}{2},{\it\chi})$ of a Dirichlet $L$-function of a character ${\it\chi}$ to a prime power modulus $q=p^{n}$ of the form $L(\frac{1}{2},{\it\chi})\ll p^{r}q^{{\it\theta}+{\it\epsilon}}$ with a fixed $r$ and ${\it\theta}\approx 0.1645<\frac{1}{6}$, breaking the long-standing Weyl exponent barrier. In fact, we develop a general new theory of estimation of short exponential sums involving $p$-adically analytic phases, which can be naturally seen as a $p$-adic analogue of the method of exponent pairs. This new method is presented in a ready-to-use form and applies to a wide class of well-behaved phases including many that arise from a stationary phase analysis of hyper-Kloosterman and other complete exponential sums.

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