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equivalence section: no need to talk about p-adic valuations here |
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Where ||''q''||<sub>T1</sub> is the [[Generalized Tenney norms and Tp interval space #The Tenney Norm (T1 norm)|tenney norm]] of ''q'' in monzo form, and v<sub>''p''</sub>(''q'') is the [[Wikipedia: P-adic order|''p''-adic valuation]] of ''q''. | Where ||''q''||<sub>T1</sub> is the [[Generalized Tenney norms and Tp interval space #The Tenney Norm (T1 norm)|tenney norm]] of ''q'' in monzo form, and v<sub>''p''</sub>(''q'') is the [[Wikipedia: P-adic order|''p''-adic valuation]] of ''q''. | ||
The function sopfr (''nd'') is the [https://mathworld.wolfram.com/SumofPrimeFactors.html "sum of prime factors with repetition"] of ''n''·''d''. Equivalently, this is the L<sub>1</sub> norm on monzos, but where each prime is weighted by ''p'' rather than log (''p'') | The function sopfr (''nd'') is the [https://mathworld.wolfram.com/SumofPrimeFactors.html "sum of prime factors with repetition"] of ''n''·''d''. Equivalently, this is the L<sub>1</sub> norm on monzos, but where each prime is weighted by ''p'' rather than log (''p''). | ||
Some useful identities: | Some useful identities: | ||