OAI/NumberTheory/Ostmann/Preliminaries/CosecantKernel.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

The cosecant kernel in the sharp additive large sieve

The finite-kernel identity is equation (3.6) of Montgomery--Vaughan, Hilbert's inequality, JLMS (2) 8 (1974), 73--82. The scalar majorant is Lemma 1 there. Only these concrete trigonometric statements are used.

  1. def OAI.Ostmann.cosecantKernel line 16
  2. def OAI.Ostmann.cotangentKernel line 17
  3. theorem OAI.Ostmann.cosecantKernel_self line 20
  4. theorem OAI.Ostmann.cotangentKernel_self line 23
  5. theorem OAI.Ostmann.cosecantKernel_skew line 26
  6. theorem OAI.Ostmann.cotangentKernel_skew line 30
  7. theorem OAI.Ostmann.cosecantKernel_triple line 34
  8. theorem OAI.Ostmann.cos_quartic_upper line 47
  9. theorem OAI.Ostmann.sine_cosecant_majorant line 64