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pro vyhledávání: '"Garvan, F. G."'
Autor:
Garvan, F. G., Sarma, Rishabh
At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. Many of Ramanujan's mock theta functions can be written in terms of $R(\
Externí odkaz:
http://arxiv.org/abs/2301.08960
Autor:
Garvan, F. G., Sarma, Rishabh
Publikováno v:
Ramanujan Journal; Dec2024, Vol. 65 Issue 4, p1883-1939, 57p
Autor:
Garvan, F. G.
New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of weight 3/2. We show that a normalized form of the g
Externí odkaz:
http://arxiv.org/abs/1011.1957
Autor:
Garvan, F. G.
Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan's partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-typ
Externí odkaz:
http://arxiv.org/abs/1011.1955
Autor:
Garvan, F. G.
Andrews' spt-function can be written as the difference between the second symmetrized crank and rank moment functions. Using the machinery of Bailey pairs a combinatorial interpretation is given for the difference between higher order symmetrized cra
Externí odkaz:
http://arxiv.org/abs/1008.1207
Autor:
Garvan, F. G.
In 2003, Hammond and Lewis defined a statistic on partitions into 2 colors which combinatorially explains certain well known partition congruences mod 5. We give two analogs of Hammond and Lewis's birank statistic. One analog is in terms of Dyson's r
Externí odkaz:
http://arxiv.org/abs/0909.4892
Autor:
Garvan, F. G.
Let spt(n) denote the total number of appearances of smallest parts in the partitions of n. Recently, Andrews showed how spt(n) is related to the second rank moment, and proved some surprising Ramanujan-type congruences mod 5, 7 and 13. We prove a ge
Externí odkaz:
http://arxiv.org/abs/0710.5793
Autor:
Atkin, A. O. L., Garvan, F. G.
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
Comment: 24 pages
Comment: 24 pages
Externí odkaz:
http://arxiv.org/abs/math/0208050
Autor:
GARVAN, F. G.
Publikováno v:
Transactions of the American Mathematical Society, 2012 Sep 01. 364(9), 4847-4873.
Externí odkaz:
http://dx.doi.org/10.1090/S0002-9947-2012-05513-9