An analogue of Landau-Walfisz theorem
| Autor: | G. Sudhaamsh Mohan Reddy, S. Srinivas Rau |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | AIP Conference Proceedings. |
| ISSN: | 0094-243X |
| Popis: | Let d be a squarefree integer. We prove that (i) ∑nμ(n)nd(n′) converges to zero, where n′ is the product of prime divisors of n with (dn)=+1. We use the Prime Number Theorem. (ii) ∏(dp)=+1(1−1ps) is not analytic ar s=1, nor is ∏(dp)=−1(1−1ps). (iii)The convergence (i) leads to a proof that asymptotically half the squarefree ideals have an even number of prime ideal factors (analogue of Ramanujan's assertion). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|