Damus
John Carlos Baez · 12w
Even if we go up to 1000 ≤ x ≤ 1100, we see the simple function 1/(1 - 2⁻ˢ)(1 - 3⁻ˢ)(1 - 5⁻ˢ) (where s = ½ + ix ) making a noble attempt to mimic the biggest peaks in the Riemann z...
John Carlos Baez profile picture
On the critical line, the Euler product does not even converge to the Riemann zeta function. So why does the product of its first few factors do a decent job of capturing the Riemann zeta function's peaks?

I haven't read about this phenomenon anywhere - have you? This paper sound promising, but it doesn't actually discuss what's happening on the critical line:

arxiv.org/abs/0704.3448

😢

(3/n, n = 3)
1
Skewray Research (ZF¬C) · 12w
nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqt54hp5 Sounds like an asymptotic expansion, right? https://en.wikipedia.org/wiki/Asymptotic_expansion