Cote n° 162-6 · pages 1–4 · 14 displayed formulas · [Documents isolés] : notes manuscrites (s.d.).
Inventory dating : s.d.
Édition de démonstration

batch 1 · p. 1 — read it beside the facsimile1 / 14 · 9 distinct symbols, 20 written
\[\gamma_{\mathbb{R}}(s) = \pi^{\frac{s}{2}}\,\Gamma\!\left(\frac{s}{2}\right)\]
LaTeX source
\[
\gamma_{\mathbb{R}}(s) = \pi^{\frac{s}{2}}\,\Gamma\!\left(\frac{s}{2}\right)
\]
batch 1 · p. 1 — read it beside the facsimile2 / 14 · 10 distinct symbols, 20 written
\[\gamma_{\mathbb{C}}(s) = \tfrac{1}{2}\,\ill\,(2\pi)^{s}\,\Gamma(s)\]
LaTeX source
\[
\gamma_{\mathbb{C}}(s) = \tfrac{1}{2}\,\ill\,(2\pi)^{s}\,\Gamma(s)
\]
batch 1 · p. 1 — read it beside the facsimile3 / 14 · 20 distinct symbols, 75 written
\[\prod_{p < q} \gamma_{\mathbb{C}}(s-p)^{h(p,q)} \cdot \begin{cases} h_{p}^{+} : F = (-1)^{p}\\ h_{p}^{-} : F = -(-1)^{p}\\ \gamma_{\mathbb{R}}(s-p)^{h_{p}^{+}}\ \gamma_{\mathbb{R}}(s-p+1)^{h_{p}^{-}} \end{cases}\]
LaTeX source
\[
\prod_{p < q} \gamma_{\mathbb{C}}(s-p)^{h(p,q)} \cdot
\begin{cases}
h_{p}^{+} : F = (-1)^{p}\\
h_{p}^{-} : F = -(-1)^{p}\\
\gamma_{\mathbb{R}}(s-p)^{h_{p}^{+}}\ \gamma_{\mathbb{R}}(s-p+1)^{h_{p}^{-}}
\end{cases}
\]
batch 1 · p. 1 — read it beside the facsimile4 / 14 · 11 distinct symbols, 22 written
\[\prod_{p,q} \gamma_{\mathbb{C}}\bigl(s - \inf(p,q)\bigr)^{h(p,q)}\]
LaTeX source
\[
\prod_{p,q} \gamma_{\mathbb{C}}\bigl(s - \inf(p,q)\bigr)^{h(p,q)}
\]
batch 1 · p. 2 — read it beside the facsimile5 / 14 · 8 distinct symbols, 15 written
\[\mathrm{gal}(E/\mathbb{Q}) \;-\; C(E)\]
LaTeX source
\[
\mathrm{gal}(E/\mathbb{Q}) \;-\; C(E)
\]
batch 1 · p. 2 — read it beside the facsimile6 / 14 · 17 distinct symbols, 34 written
\[\begin{array}{c|l} \sigma & \sigma z \sigma^{-1} = \bar{z}\\ \mathbb{C}^{*} & \sigma^{2} = (-1) \end{array}\]
LaTeX source
\[
\begin{array}{c|l}
\sigma & \sigma z \sigma^{-1} = \bar{z}\\
\mathbb{C}^{*} & \sigma^{2} = (-1)
\end{array}
\]
batch 1 · p. 2 — read it beside the facsimile7 / 14 · 9 distinct symbols, 16 written
\[H^{2}(\mathbb{Z}/2, \mathbb{C}^{*}) = \mathbb{Z}/2\]
LaTeX source
\[
H^{2}(\mathbb{Z}/2, \mathbb{C}^{*}) = \mathbb{Z}/2
\]
batch 1 · p. 2 — read it beside the facsimile8 / 14 · 12 distinct symbols, 22 written
\[H(D(E), \mathbb{R}) \quad \sigma \quad \Big|\ \sigma\ \Big|\ \sigma^{2} = +1\]
LaTeX source
\[
H(D(E), \mathbb{R}) \quad \sigma \quad \Big|\ \sigma\ \Big|\ \sigma^{2} = +1
\]
batch 1 · p. 3 — read it beside the facsimile9 / 14 · 7 distinct symbols, 11 written
\[N : S_{E} \longrightarrow S_{\mathbb{Q}} \longrightarrow \mathbb{G}_{m}\]
LaTeX source
\[
N : S_{E} \longrightarrow S_{\mathbb{Q}} \longrightarrow \mathbb{G}_{m}
\]
batch 1 · p. 3 — read it beside the facsimile10 / 14 · 14 distinct symbols, 32 written
\[(x, (y_{\alpha})) \longmapsto x \cdot \prod_{\alpha \neq \infty} \lVert y_{\alpha} \rVert \cdot \prod_{\alpha = \infty} \mathrm{sign}(y_{\alpha})\]
LaTeX source
\[
(x, (y_{\alpha})) \longmapsto x \cdot \prod_{\alpha \neq \infty} \lVert y_{\alpha} \rVert \cdot \prod_{\alpha = \infty} \mathrm{sign}(y_{\alpha})
\]
batch 1 · p. 3 — read it beside the facsimile11 / 14 · 9 distinct symbols, 22 written
\[C(E) \longrightarrow S_{E}(\mathbb{A}) \longrightarrow S_{E}(\mathbb{R}) \longrightarrow \mathbb{R}^{*}\]
LaTeX source
\[
C(E) \longrightarrow S_{E}(\mathbb{A}) \longrightarrow S_{E}(\mathbb{R}) \longrightarrow \mathbb{R}^{*}
\]
batch 1 · p. 3 — read it beside the facsimile12 / 14 · 7 distinct symbols, 9 written
\[(-1 \neq \lVert -1 \rVert)\]
LaTeX source
\[
(-1 \neq \lVert -1 \rVert)
\]
batch 1 · p. 4 — read it beside the facsimile13 / 14 · 11 distinct symbols, 19 written
\[L_{v}(M \otimes T, s) = L_{v}(M)(s \pm 1)\]
LaTeX source
\[
L_{v}(M \otimes T, s) = L_{v}(M)(s \pm 1)
\]
batch 1 · p. 4 — read it beside the facsimile14 / 14 · 9 distinct symbols, 21 written
\[\gamma_{\mathbb{R}}(s)\, \gamma_{\mathbb{R}}(s+1) = \gamma_{\mathbb{C}}(s)\]
LaTeX source
\[
\gamma_{\mathbb{R}}(s)\, \gamma_{\mathbb{R}}(s+1) = \gamma_{\mathbb{C}}(s)
\]