Matching Tag: algebraic-independence
Algebraic-independence conjecture. The numbers ln p 1 , … , ln p m \ln p_1,\ldots,\ln p_m ln p 1 , … , ln p m ψ \psi ψ
Algebraic independence conjecture for odd zeta values. The numbers π , ζ ( 3 ) , ζ ( 5 ) , ζ ( 7 ) , ζ ( 9 ) , … \pi,\zeta(3),\zeta(5),\zeta(7),\zeta(9),\ldots π , ζ ( 3 ) , ζ ( 5 ) , ζ ( 7 ) , ζ ( 9 ) , … Q \mathbb{Q} Q
Let T p ( z ) T_p(z) T p ( z ) p p p p 1 , p 2 , … , p m p_1,p_2,\dots,p_m p 1 , p 2 , … , p m α 1 , α 2 , … , α m \alpha_1,\alpha_2,\dots,\alpha_m α 1 , α 2 , … , α m
Let r ≥ 1 r\geq 1 r ≥ 1 b 1 , … , b r b_1,\ldots,b_r b 1 , … , b r i i i 1 ≤ i ≤ r 1\leq i\leq r 1 ≤ i ≤ r ξ i \xi_i ξ i
Let Z ‾ \overline{\mathfrak{Z}} Z Q ‾ \overline{\mathbb{Q}} Q Z ‾ w \overline{\mathfrak{Z}}_w Z w Q ‾ \overline{\mathbb{Q}} Q
Let α 1 , … , α n \alpha_1,\ldots,\alpha_n α 1 , … , α n log α 1 , … , log α n \log \alpha_1,\ldots,\log \alpha_n log α 1 , … , log α n Q \mathbb{Q} Q
For k ≥ 0 k\ge0 k ≥ 0 \calA 1 \calA_1 \calA 1 k ≥ 2 k\ge2 k ≥ 2 k k k \calA 1 \calA_1 \calA 1 \gb 1 = 1 \gb_1=1 \gb 1 = 1 n 1 , … , n r ∈ N n_1,\dots,n_r\in\N n 1 , … , n r ∈ N
Let L \mathcal{L} L Q \mathbb Q Q n ≥ 2 n\geq 2 n ≥ 2 L D n Q {\sf LD}_n^{\mathbb Q} LD n Q n n n
Let Λ ⊂ C \Lambda\subset\mathbb{C} Λ ⊂ C λ ∈ Λ ∖ { 0 } \lambda\in\Lambda\setminus\{0\} λ ∈ Λ ∖ { 0 } ω ∈ C ∖ ( Q λ ∪ Λ ) \omega\in\mathbb{C}\setminus(\mathbb{Q}\lambda\cup\Lambda) ω ∈ C ∖ ( Q λ ∪ Λ )
Let ρ \rho ρ F q [ t ] \mathbb{F}_q[t] F q [ t ] k ‾ \overline{k} k F δ 1 , … , F δ s F_{\delta_1},\dots,F_{\delta_s} F δ 1 , … , F δ s C ∞ \mathbb{C}_\infty C ∞
Magnus trace map surjectivity conjecture. The map M a g T r I \mathsf{MagTr}_{\mathcal{I}} MagTr I
