Arithmetic correlations over large finite fields
| Autor: | Edva Roditty-Gershon, Jon P Keating |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Von Mangoldt function Mathematics - Number Theory General Mathematics 010102 general mathematics Mathematical analysis Divisor function 0102 computer and information sciences 01 natural sciences Finite field 010201 computation theory & mathematics FOS: Mathematics Arithmetic function Analytic number theory Limit (mathematics) Number Theory (math.NT) 0101 mathematics Remainder Function field Mathematics |
| Zdroj: | Keating, J P & Roditty-Gershon, E 2016, ' Arithmetic Correlations Over Large Finite Fields ', International Mathematics Research Notices, vol. 2016, no. 3, pp. 860-874 . https://doi.org/10.1093/imrn/rnv157 |
| DOI: | 10.1093/imrn/rnv157 |
| Popis: | The auto-correlations of arithmetic functions, such as the von Mangoldt function, the M\"obius function and the divisor function, are the subject of classical problems in analytic number theory. The function field analogues of these problems have recently been resolved in the limit of large finite field size $q$. However, in this limit the correlations disappear: the arithmetic functions become uncorrelated. We compute averages of terms of lower order in $q$ which detect correlations. Our results show that there is considerable cancellation in the averaging and have implications for the rate at which correlations disappear when $q \rightarrow\infty$; in particular one cannot expect remainder terms that are of the order of the square-root of the main term in this context. Comment: The paper has been accepted by IMRN |
| Databáze: | OpenAIRE |
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