Add to ORKGAbstract. We develop a substantial enhancement of the efficient congru-encing method to estimate Vinogradov’s integral of degree k for moments of order 2s, thereby obtaining for the first time near-optimal estimates for s> 58k 2. There are numerous applications. In particular, when k is large, the anticipated asymptotic formula in Waring’s problem is established for sums of s kth powers of natural numbers whenever s> 1.543k2. 1
We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem fo...
We obtain new upper bounds for the number of integral solutions of a complete system of sym-metric e...
Abstract. Recent progress on Vinogradov’s mean value theorem has resulted in improved estimates for ...
Abstract. We apply multigrade efficient congruencing to estimate Vino-gradov’s integral of degree k ...
Abstract. We enhance the efficient congruencing method for estimating Vinogradov’s integral for mome...
Abstract. We enhance the efficient congruencing method for estimating Vinogradov’s integral for mome...
Abstract. We apply a variant of the multigrade efficient congruencing method to estimate Vinogradov’...
This document is made available in accordance with publisher policies. Please cite only the publishe...
Abstract. We describe mean value estimates for exponential sums of degree exceeding 2 that approach ...
This document is made available in accordance with publisher policies. Please cite only the publishe...
We give a slight refinement to the process by which estimates for exponential sums are extracted fro...
We give a slight refinement to the process by which estimates for exponential sums are extracted fro...
We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This ...
Abstract. We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov’s...
We use a generalisation of Vinogradov's mean value theorem of Parsell et al.['Near-optimal mean valu...
We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem fo...
We obtain new upper bounds for the number of integral solutions of a complete system of sym-metric e...
Abstract. Recent progress on Vinogradov’s mean value theorem has resulted in improved estimates for ...
Abstract. We apply multigrade efficient congruencing to estimate Vino-gradov’s integral of degree k ...
Abstract. We enhance the efficient congruencing method for estimating Vinogradov’s integral for mome...
Abstract. We enhance the efficient congruencing method for estimating Vinogradov’s integral for mome...
Abstract. We apply a variant of the multigrade efficient congruencing method to estimate Vinogradov’...
This document is made available in accordance with publisher policies. Please cite only the publishe...
Abstract. We describe mean value estimates for exponential sums of degree exceeding 2 that approach ...
This document is made available in accordance with publisher policies. Please cite only the publishe...
We give a slight refinement to the process by which estimates for exponential sums are extracted fro...
We give a slight refinement to the process by which estimates for exponential sums are extracted fro...
We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This ...
Abstract. We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov’s...
We use a generalisation of Vinogradov's mean value theorem of Parsell et al.['Near-optimal mean valu...
We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem fo...
We obtain new upper bounds for the number of integral solutions of a complete system of sym-metric e...
Abstract. Recent progress on Vinogradov’s mean value theorem has resulted in improved estimates for ...