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Award ID contains: 2409803

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  1. ; ; ; (, International Mathematics Research Notices)
    Abstract We prove the sharp mixed norm $$(l^{2}, L^{q}_{t}L^{r}_{x})$$ decoupling estimate for the paraboloid in $d + 1$ dimensions. 
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  2. (, Contemporary mathematics American Mathematical Society)
    The goal of this expository paper is to provide an introduction to decoupling by working in the simpler setting of decoupling for the parabola over Q_p. Over Q_p, commonly used heuristics in decoupling are significantly easier to make rigorous over Q_p than over R and such decoupling theorems over Q_p are still strong enough to derive interesting number theoretic conclusions. 
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    Accepted Manuscript Full Text Available
  3. ; ; ; ; ; (, Mathematika)
    We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely solution counting in older partial progress on Vinogradov's mean value theorem corresponds to in Fourier decoupling theory. 
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    Full Text Available