AN IDENTITY OF RAMANUJAN, AND APPLICATIONS AMS Classification 11P83
, 2008 Dedicated to Dick Askey on the occasion of his 65th ...
Michael D. Hirschhorn
core
Two congruences involving 4-cores
, 1996 . The goal of this paper is to prove two new congruences involving 4-cores using elementary techniques; namely, if a4(n) denotes the number of 4-cores of n, then a4(9n+2) j 0 (mod 2) and a4(9n + 8) j 0 (mod 4).
Michael D. Hirschhorn, James A. Sellers
core
Ramanujan's Theta Functions and Parity of Parts and Cranks of Partitions. [PDF]
Ann Comb, 2023 Banerjee K, Dastidar MG.
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© Hindawi Publishing Corp. CONGRUENCES IN ORDERED PAIRS OF PARTITIONS
, 2003 Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank.
Richard Lewis, Paul Hammond
core
On sums of coefficients of polynomials related to the Borwein conjectures. [PDF]
Ramanujan J, 2022 Goswami A, Pantangi VRT.
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©Electronic Publishing House q-SERIES, ELLIPTIC CURVES, AND ODD VALUES OF THE PARTITION FUNCTION
, 1997 . Let p(n) be the number of partitions of an integer n. Euler proved the following recurrence for p(n): p(n) = (−1) k+1 p n−ω(k) +p n−ω(−k) k=1 where ω(k) = 3k2 +k /2.
Nicholas Eriksson
core
A single-variable proof of the omega SPT congruence family over powers of 5. [PDF]
Ramanujan J, 2023 Smoot NA.
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The Cause of Lead Poisoning in the Tinning of Metals. [PDF]
J Hyg (Lond), 1908 Duckering GE.
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Explaining unforeseen congruence relationships between PEND and POND partitions via an Atkin-Lehner involution. [PDF]
Ramanujan JSellers JA, Smoot NA.
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Computer-assisted construction of Ramanujan-Sato series for 1 over π. [PDF]
Ramanujan JHemmecke R, Paule P, Radu CS.
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