Arithmetic properties of the partition function

By Scott Ahlgren, M. Boylan. 2003

112 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/d5195c7bb58eb2c9623648fa442f567802aa85cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Congruences for Andrews' Smallest Parts Partition Function and New Congruences for Dyson's Rank (2007, background): “We note that Chua’s result was extended to prime power moduli by Ahlgren and Boylan [2].”
ℓ-Divisibility of ℓ-regular partition functions (2009, background): “for every nonnegative integer n. Recently K. Ono [4] showed that there exist congruences for p(n) modulo every prime greater than 3, and S. Ahlgren and M. Boylan [ 1 ] demonstrated the uniqueness of the Ramanujan congruences among these by proving that if � is prime and there exists an integer a suc”
RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION (2010, background): “• In [4], Ahlgren and Boylan proved a beautiful theorem which states that there are no simple congruences for p(n) apart from those with moduli 5, 7, and 11.”
Basic Hypergeometric Series (2004, background): “In general, if β is a prime, then the congruence with some fixed γ ∈ N p(βn + γ) ≡β 0 for all n ∈ N is called the Ramanujan congruence modulo β. Ahlgren and Boylan (2003) confirmed recently that the three congruences displayed above are the only Ramanujan ones.”
Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms (2011, unknown): “For example, if n = 2, then −24n + 1 = −47, and we have that h(−47) = 5 and Q2 = {[6, 1, 2], [12, 1, 1], [18, 13, 3], [24, 25, 7], [36, 49, 17]}, where [a, b, c] := ax + bxy + cz.”
ℓ-Adic properties of the partition function☆☆☆ (2012, methodology): “To prove Theorem 1.3 we combine these ideas with the works of Ahlgren and Boylan, Garvan, and Yang related to Ramanujan-type congruences.”