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6 votes

Global character of ABC/Szpiro inequalities

This is not an answer to the question but too long for a comment. It is interesting to ask if one can prove the ABC inequality just for the tuple $(1,p^n,1+p^n)$ directly for fixed $p$. ABC says $\...
CHUAKS's user avatar
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27 votes

Consequences of Kirti Joshi's new preprint about p-adic Teichmüller theory on the validity of IUT and on the ABC conjecture

My response to Mochizuki's Comments on my papers [Preprints: Construction of Arith. Holo. Strs I, II, II(1/2), III, IV. I will restrict myself to mathematics. My work shows that Mochizuki's [IUT 1-3] ...
Kirti Joshi's user avatar
0 votes
Accepted

The d(abc)-theorem, the abc-conjecture and positive definite kernels over the natural numbers?

This is wrong for the divisor counting function $\sigma_0$ and $n=73$ as the Gram matrix has determinant $<0$.
mathoverflowUser's user avatar
4 votes
Accepted

abc-conjecture and positive definite kernels, again?

The conjecture about the positive definiteness of the kernel above is wrong as one has $\det(G_{192})<0$: ...
mathoverflowUser's user avatar

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