A singular series average and the zeros of the Riemann zeta-function
| Autor: | Ade Irma Suriajaya, Daniel A. Goldston |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Mathematics::Functional Analysis Algebra and Number Theory Series (mathematics) Mathematics - Number Theory Mathematics::Number Theory Mathematics::Classical Analysis and ODEs Term (logic) Riemann zeta function symbols.namesake Riemann hypothesis Riesz mean Goldbach's conjecture symbols FOS: Mathematics 11N05 11M26 Asymptotic formula Number Theory (math.NT) Computer Science::Databases Mathematics |
| Popis: | We show that the Riesz mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures has an asymptotic formula with an error term that can be expressed as an explicit formula that depends on the zeros of the Riemann zeta-function. Unconditionally this error term can be shown to oscillate, while conditionally it can be shown to oscillate between sharp bounds. 14 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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