The avatar for @follymath
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Public
Edited
Dec 27, 2022
Fork of Arbuckle
1 star
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s = ℂ(ℜs,ℑs)
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r = ℂ(1,0).sub(s)
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ζ_s = ζ(s)
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ζ_s_q = ζ(s,q)
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rotation_factor = (x) => {
if (x > ℑs/π) return 2*π * x/(ℑs/π)
return 0
}
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s.im / (2 * Math.PI)
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// viewof ℑs = slider({
// title: 'Im part of zeta arg',
// min: 150,
// max: 400,
// value: 223.222419286,
// // step: 'any',
// })

// ℑs1 = 63 * π - π/2

// ℑs1 = 77*π+0.122007
// ℑs1 = 223.222419286
// ℑs1 = 231.64
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hspin = (t) => π * t * 2 // 4 * π * t / Math.round(4 * π * t / ℑs)
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Math.round(4 * q * π / ℑs) / 2
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data_3d = {
const data = []
data.push(build_series(ζ_s_partials, {
name: 'ζ(s,_)',
visible: 'legendonly'
}))
data.push(build_series(ζ_s_partials_norm, {
name: 'ζ*(s,_)'
}))

// add normalized hurwitz zeta point
data.push(build_point(ζ_s_q.mul(χ_r), q, {
name: 'ζ*(s,q)',
visible: 'legendonly'
}))

// add normalized, derotated point
data.push(build_point(
ζ_s_q_normalized,
q,
{
name: 'ζ**(s,q)',
marker: { color: 'purple' }
}
))

if (plot_3d && plot_3d.data) plot_3d.data.forEach((d,i) => {
const cur = data[i]
if (cur) cur.visible = d.visible || cur.visible
})

return data
}
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ζ_next = (s, a, s_a) => (s_a || ζ(s,a)).sub(ℂ(1).div(ℂ(a).pow(2).pow(ℂ(s).div(2))))
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ζ_prev = (s, a, s_a) => (s_a || ζ(s,a)).add(ℂ(1).div(ℂ(a).sub(1).pow(2).pow(ℂ(s).div(2))))
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χ = (s) => ℂ(mathjs.eval('pi^(s-1/2) gamma((1-s)/2) / gamma(s/2)', { s }))
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