Ramanujan's lost notebook

By George E. Andrews, Bruce C. Berndt. 2012

76 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/a7768e471903624f7b5589fb1f42996ba7106505

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In Algebra and Number Theory

1. Frank G. Garvan
2. George E. Andrews
3. Jie Frye
4. Kathrin Bringmann
5. Karl Mahlburg
6. V. Spiridonov
7. Jeremy Lovejoy
8. Robert Osburn

In Theoretical Computer Science

1. George E. Andrews

Citations in the corpus

• Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q) (2015, background): “(14) Finally, we note Bailey’s 10φ9 transformation ([6] Equation (2.10)), ([17] Equation (6.3)): lim N→∞ 10φ9 ⎛ ⎝a, q2 √ a, −q2√a, p1, p1q, p2, p2q, f , q−2N , q−2N+1 √ a, −√a, aq 2 p1 , aq p1 , aq2 p2 , aq p2 , aq2 f , aq2N+2, aq2N+1 ; q2, a3q4N+3 p21p 2 2f ⎞ ⎠ = (aq; q)∞ ( aq p1p2 ; q ) ∞( aq p1 ;”
• Automatic Proof of Theta-Function Identities (2018, background): “EXAMPLE: > Gamma1ModFunc(L1,4); 1 > xprint := true: > Gamma1ModFunc(L1,4); * starting Gamma1ModFunc with L=[[4, 1, 16], [4, 2, -4]] and N=4 All n are divisors of 4 val0=2 which is even. valinf=0 which is even.”
• q-Orthogonal polynomials, Rogers-Ramanujan identities, and mock theta functions (2012, background): “The upshot of this neglect is that a number of Bailey pairs of great significance in the study of mock theta functions [3], [4], [9], [10] had a purely empirical discovery and rather ad hoc proofs.”