Timeline for On modified Euler product
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 5, 2021 at 15:46 | comment | added | Zaza | @davidlowryduda thank you for the comment. As you can see in the post I want value for c=1/√e | |
| Mar 5, 2021 at 15:36 | comment | added | davidlowryduda | There is a slightly subtle point concerning the convergence of $\log (1 - cp^{-s})$. The log expansion here is valid only for $\lvert cp^{-s} \rvert < 1$, and otherwise the expansion diverges. What this means is that to study $F(s)$ with this at a generic $s$ with $\mathrm{Re} s > 0$, it might be necessary to separate out small primes and handle them on their own. Annoying bookkeeping. But if $c < \sqrt{2}$, for example, then this should work as written to understand $F(1/2)$. | |
| Mar 5, 2021 at 14:00 | comment | added | Zaza | thank you for the answer. But I really couldn't fully understand what do you mean by finite sums for analytic continuation. Are you implying that we should take first n terms for analytic continuation to avoid divergence of infinite sum? Because I want to calculate its value at 1/2 | |
| Mar 2, 2021 at 7:09 | history | answered | Ralph Furman | CC BY-SA 4.0 |