• Corpus ID: 245329788

Congruences like Atkin's for the partition function

  title={Congruences like Atkin's for the partition function},
  author={Scott Ahlgren and Patrick Brodie Allen and Shiang Tang},
. Let p ( n ) be the ordinary partition function. In the 1960s Atkin found a number of examples of congruences of the form p ( Q 3 ℓn + β ) ≡ 0 (mod ℓ ) where ℓ and Q are prime and 5 ≤ ℓ ≤ 31; these lie in two natural families distinguished by the square class of 1 − 24 β (mod ℓ ). In recent decades much work has been done to understand congruences of the form p ( Q m ℓn + β ) ≡ 0 (mod ℓ ). It is now known that there are many such congruences when m ≥ 4, that such congruences are scarce (if… 
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