A proof of Subbarao's conjecture

DOI10.1515/CRELLE.2011.165zbMath1276.11165OpenAlexW2055340390WikidataQ59664812 ScholiaQ59664812MaRDI QIDQ3145928

Cristian-Silviu Radu

Publication date: 17 December 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2011.165

zbMATH Keywords

partition functionmodular formsarithmetic progressionparitySubbarao's conjecture

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Congruences for modular and (p)-adic modular forms (11F33) Elementary theory of partitions (11P81)

Related Items (21)

The partition function modulo 3 in arithmetic progressions ⋮ Linear incongruences for generalized eta-quotients ⋮ Parity of the coefficients of certain eta-quotients ⋮ Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights ⋮ On the number of even values of an eta-quotient ⋮ Hecke nilpotency for modular forms \(\bmod\, 2\) and an application to partition numbers ⋮ Variations on a result of Bressoud ⋮ Scarcity of congruences for the partition function ⋮ Parity of sums of partition numbers and squares in arithmetic progressions ⋮ Parity of the coefficients of certain eta-quotients. II: The case of even-regular partitions ⋮ Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 ⋮ On the density of the odd values of the partition function. II: An infinite conjectural framework ⋮ Incongruences for modular forms and applications to partition functions ⋮ A mod \(\ell\) Atkin-Lehner theorem and applications ⋮ On the density of the odd values of the partition function ⋮ An extensive analysis of the parity of broken 3-diamond partitions ⋮ Congruences for modular forms and generalized Frobenius partitions ⋮ Proof of a conjecture by Ahlgren and Ono on the non-existence of certain partition congruences ⋮ Congruences of Hurwitz class numbers on square classes ⋮ Relations among Ramanujan-type congruences. I ⋮ New parity results of sums of partitions and squares in arithmetic progressions

Cites Work

• An algorithmic approach to Ramanujan's congruences
• On the parity of \(p(n)\). II
• On congruence properties of the partition function
• Distribution of the partition function modulo composite integers \(M\)
• Distribution of the partition function modulo \(m\)
• PARITY OF THE PARTITION FUNCTION IN ARITHMETIC PROGRESSIONS, II
• Note on the Parity of the Partition Functions.
• The Components of Modular Forms
• Some Remarks on the Partition Function

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