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Add the Hardy--Littlewood bound mu(1/2) <= 1/6 to the literature - #202

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Add the Hardy--Littlewood bound mu(1/2) <= 1/6 to the literature#202
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:add-hardy-littlewood-mu-bound

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The zeta growth chapter opens its μ(1/2) table with Hardy--Littlewood (1923), μ(1/2) ≤ 1/6, from the exponent pair (1/6, 2/3). The Python literature set has no such hypothesis: the critical-line list starts at Walfisz (1924), and both generated sequences (van der Corput and Hardy--Littlewood) start at n = 4, one term past the σ = 1/2 member.

Everything that asks for that bound is broken as a result:

  • literature.add_bounds_mu_classic adds None to the hypothesis set;
  • derived.prove_hardy_littlewood_mu_bound and examples.mu_bound_examples both raise AttributeError: 'NoneType' object has no attribute 'desc'.

One entry, citing hardy_littlewood_1923 which is already in references.bib.

After it, derived.prove_hardy_littlewood_mu_bound() runs and reproves the bound the way the blueprint describes:

We will reprove Hardy--Littlewood bound on \mu(1/2) (\mu(1/2) \leq 1/6).
We have Derived exponent pair (1/2, 1/2) ... van der Corput B transform.
This implies Derived exponent pair (1/6, 2/3) ... van der Corput A transform.
This implies Derived bound on \mu(1/2): \mu(1/2) \leq 1/6.

tests/test_exppair.py, tests/test_ep_to_zd.py and tests/test_region.py still pass with the extra hypothesis in the set. (tests/test_all.py as a whole does not run on main; that is #200.)

The zeta growth chapter lists Hardy--Littlewood (1923) as the first
entry of the mu(1/2) table, but the Python literature set has no such
hypothesis: the critical-line list starts at Walfisz (1924), and the two
generated sequences both start at n = 4, which is past the term that
gives sigma = 1/2.

Everything that asks for it therefore fails. literature.add_bounds_mu_classic
adds None to the hypothesis set, and derived.prove_hardy_littlewood_mu_bound
and examples.mu_bound_examples both die on
"'NoneType' object has no attribute 'desc'".

With the entry in place, prove_hardy_littlewood_mu_bound reproves the
bound from the trivial exponent pair via B then A, exactly as the
blueprint describes.
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