Manuscript I-B-VP-0@1 · I-B-VP-0-v1.tex · section · 8a9d0682

An independent exact quotient check

An independent exact quotient check · lines 951–975

I-B-VP-0@1#eq:quotientkernel

For

α = \frac{1}{N}, β = \frac{p}{N}, N \geq 2, p \in {0, \dots, N - 1},

the character is compatible with the cyclic quotient. The Friedrichs Euclidean kernel is the finite character-weighted image kernel CheungIBG (:structure). In a developing parallel frame, its regular part is

H_{E, p / N} (X, X^{'}) = k = 1 \sum^{N - 1} \frac{e ^{2 π i p k / N}}{4 π ^{2} ∣ X _{E} - R _{k} X ^{'} _{E} ∣ ^{2}},

where $R_{k}$ rotates the transverse plane by $2 π k / N$ and fixes $τ, z$ . The sum contains the full quotient images, also for even $N$ .

Displayed formulas in this passage

I-B-VP-0@1#eq:quotientkernel · line 965
$H_{E, p / N} (X, X^{'}) = k = 1 \sum^{N - 1} \frac{e ^{2 π i p k / N}}{4 π ^{2} ∣ X _{E} - R _{k} X ^{'} _{E} ∣ ^{2}},$
unlabeled · line 955
$α = \frac{1}{N}, β = \frac{p}{N}, N \geq 2, p \in {0, \dots, N - 1},$

An independent exact quotient check

Displayed formulas in this passage

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