The meaning of Ramanujan now and for the future

DOI10.1007/s11139-009-9162-4zbMath1195.11004OpenAlexW2023534196MaRDI QIDQ969414

George E. Andrews

Publication date: 7 May 2010

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-009-9162-4

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Research exposition (monographs, survey articles) pertaining to number theory (11-02) History of number theory (11-03) Elementary theory of partitions (11P81)

Uses Software

• Omega

Cites Work

• Ramanujan's ``Lost notebook. VIII: The entire Rogers-Ramanujan function
• Ramanujan's ``lost notebook. IX: The partial theta function as an entire function
• Zeros of entire functions and a problem of Ramanujan
• Combinatorics of generalized \(q\)-Euler numbers
• Zeros of generalized Rogers-Ramanujan series: asymptotic and combinatorial properties
• Ramanujan's lost notebook. V: Euler's partition identity
• Inverse polynomial expansions of Laurent series
• Ramanujan's ``lost notebook. II: Theta-function expansions
• On the difference of successive Gaussian polynomials
• \(q\)-series identities and values of certain \(L\)-functions
• A Maple package for symmetric functions
• Engel expansions and the Rogers-Ramanujan identities
• Distribution of the partition function modulo \(m\)
• Extension of Abel's Lemma with \(q\)-series implications
• Eulerian series as modular forms
• Mock theta functions, weak Maass forms, and applications
• A $q$-series identity and the arithmetic of Hurwitz zeta functions
• Partition congruences and the Andrews-Garvan-Dyson crank
• Hypergeometric generating functions for values of Dirichlet and other L functions
• Proof of a conjecture of Ramanujan
• Ordered structures and partitions
• The Final Problem : An Account of the Mock Theta Functions
• MacMahon's partition analysis: The Omega package
• Vassiliev invariants and a strange identity related to the Dedekind eta-function
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