Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 17

C1  =  X + 14
C2  =  X2 + 16X + 3
C3  =  X3 + X + 14
C4  =  X4 + 7X2 + 10X + 3
C6  =  X6 + 2X4 + 10X2 + 3X + 3


ξ f Cn
b5 10X + 3 C2
b5∗ 7X + 13 C2
b7 8X + 4 C2
b7∗∗ 9X + 12 C2
b11 X + 16 C2
b11∗∗ 16X C2
b13 12 C1
b13∗ 4 C1
b15 11 C1
b15∗∗ 5 C1
b19 3 C1
b19∗∗ 13 C1
b21 9 C1
b21∗ 7 C1
b27 2X + 7 C2
b27∗∗ 15X + 9 C2
b29 6X + 5 C2
b29∗ 11X + 11 C2
b31 3X + 15 C2
b31∗∗ 14X + 1 C2
b33 6 C1
b33∗ 10 C1
b35 10 C1
b35∗∗ 6 C1
b39 11X + 11 C2
b39∗∗ 6X + 5 C2
b45 13X + 10 C2
b45∗ 4X + 6 C2
b47 9 C1
b47∗∗ 7 C1
b59 15 C1
b59∗∗ 1 C1
b71 5X + 14 C2
b71∗∗ 12X + 2 C2
b87 3 C1
b87∗∗ 13 C1
b117 3 C1
b117∗ 13 C1
c31 10X2 + 6X + 12 C3
c31∗3 15X2 + 6X + 4 C3
c31∗5 9X2 + 5X C3
f31 X5 + 14X4 + 9X3 + 10X2 + 8X + 10 C6
f31∗3 4X5 + 14X4 + 4X3 + 8X2 + 16X + 2 C6
f31∗5 3X5 + 2X4 + 5X3 + 1 C6
f31∗7 5X5 + X4 + 14X3 + 3X2 + 9X + 14 C6
f31∗11 9X5 + 9X4 + 10X3 + 8X2 + 3X + 2 C6
f31∗15 12X5 + 11X4 + 9X3 + 5X2 + 15X + 4 C6
i 13 C1
i2 7 C1
i3 7X + 5 C2
i5 5X + 6 C2
i7 16X + 9 C2
i11 2X + 16 C2
i14 6X + 14 C2
i15 6 C1
i19 7 C1
i26 5 C1
i35 4 C1
r2 11 C1
r3 11X + 3 C2
r5 3X + 7 C2
r6 2X + 16 C2
r7 13X + 2 C2
r10 16X + 9 C2
r13 8 C1
r21 2 C1
v33 14X + 5 C2
v33∗2 3X + 2 C2
v33∗5 2X + 13 C2
v33∗7 15X + 15 C2
y9 14 C1
y9∗2 7 C1
y9∗4 13 C1
y15 8X3 + 9X2 + 14X + 11 C4
y15∗2 4X3 + X2 + 14X + 4 C4
y15∗4 14X3 + X2 + 10X + 11 C4
y15∗7 8X3 + 6X2 + 13X + 9 C4
y16 9 C1
y16∗3 5 C1
y16∗5 12 C1
y16∗7 8 C1
y32 9X + 4 C2
y32∗3 4X + 15 C2
y32∗5 10X + 12 C2
y32∗7 X + 8 C2
y32∗9 16X + 9 C2
y32∗11 7X + 5 C2
y32∗13 13X + 2 C2
y32∗15 8X + 13 C2
y36 15X + 1 C2
y36∗5 12X + 11 C2
y36∗7 3X + 7 C2
y36∗11 14X + 10 C2
y36∗13 5X + 6 C2
y36∗17 2X + 16 C2
z3 12X + 2 C2
z3∗∗ 5X + 14 C2




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