Incomplete gauss sums modulo primes
| Autor: | Bryce Kerr |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Current (mathematics)
Mathematics - Number Theory Mathematics::Number Theory General Mathematics Modulo 010102 general mathematics Vinogradov Congruence relation 01 natural sciences 010101 applied mathematics Combinatorics Range (mathematics) symbols.namesake Bounding overwatch Gauss sum FOS: Mathematics symbols Number Theory (math.NT) 0101 mathematics Mean value theorem Mathematics |
| Zdroj: | The Quarterly Journal of Mathematics. 69:729-745 |
| ISSN: | 1464-3847 0033-5606 |
| Popis: | We obtain a new bound for incomplete Gauss sums modulo primes. Our argument falls under the framework of Vinogradov's method which we use to reduce the problem under consideration to bounding the number of solutions to two distinct systems of congruences. The first is related to Vinogradov's mean value theorem, although the second does not appear to have been considered before. Our bound improves on current results in the range $N\ge q^{2k^{-1/2}+O(k^{-3/2})}$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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