OAI/NumberTheory/PrimeGaps/MultiplicativeSieve.lean

GitHub source file

31 declarations, 0 contain sorry, 0 declared as axioms

  1. theorem OAI.LargePrimeGaps.conj_stdAddChar line 29
  2. theorem OAI.LargePrimeGaps.conj_gaussSum_eq_dft_inverse line 34
  3. theorem OAI.LargePrimeGaps.primitive_gauss_mul_conjugate line 43
  4. theorem OAI.LargePrimeGaps.primitive_gauss_norm_sq line 56
  5. def OAI.LargePrimeGaps.characterUnitVector line 62
  6. theorem OAI.LargePrimeGaps.conj_character_unit line 65
  7. theorem OAI.LargePrimeGaps.inner_characterUnitVector line 70
  8. theorem OAI.LargePrimeGaps.character_transform_bound line 83
  9. def OAI.LargePrimeGaps.sequenceCharacterSum line 100
  10. def OAI.LargePrimeGaps.modularFourierSum line 103
  11. theorem OAI.LargePrimeGaps.primitive_inverse line 106
  12. theorem OAI.LargePrimeGaps.multiply_sum_units line 112
  13. theorem OAI.LargePrimeGaps.primitive_character_gauss_expansion line 124
  14. theorem OAI.LargePrimeGaps.primitive_character_energy_le line 153
  15. def OAI.LargePrimeGaps.unitFrequency line 182
  16. theorem OAI.LargePrimeGaps.unitFrequency_den line 184
  17. theorem OAI.LargePrimeGaps.unitFrequency_bounds line 194
  18. def OAI.LargePrimeGaps.fareyFrequency line 199
  19. theorem OAI.LargePrimeGaps.fareyFrequency_injective line 201
  20. theorem OAI.LargePrimeGaps.modularFourierSum_eq_bvExp line 218
  21. theorem OAI.LargePrimeGaps.multiplicative_large_sieve line 235
  22. theorem OAI.LargePrimeGaps.weighted_sum_mul_sq_le line 268
  23. def OAI.LargePrimeGaps.primitiveCharacterMean line 279
  24. theorem OAI.LargePrimeGaps.primitiveCharacterMean_nonneg line 284
  25. theorem OAI.LargePrimeGaps.primitiveCharacterMean_cauchy line 291
  26. theorem OAI.LargePrimeGaps.bilinear_multiplicative_large_sieve line 320
  27. theorem OAI.LargePrimeGaps.sequenceCharacterSum_mul line 331
  28. theorem OAI.LargePrimeGaps.exponential_kernel_offdiagonal_bound line 345
  29. theorem OAI.LargePrimeGaps.residue_frequency_separation line 357
  30. theorem OAI.LargePrimeGaps.modularFourierSum_one line 377
  31. theorem OAI.LargePrimeGaps.primitive_polya_vinogradov line 395