Ramanujan's Lost Notebook: Part I

789 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On the dual nature of partial theta functions and Appell-Lerch sums (2012, methodology): “ested reader, we point out that (4.1) yields as special cases the two partial theta function identities found in Lawrence and Zagier’s work on quantum invariants of 3-manifolds [22]. 4.1. Entry 6.3.2 [8], also [27, p. 7]. For a6= 0, X∞ n=0 qn (−aq,−q/a)n = (1+a) X∞ n=0 a3 nq n(3 +1)/2(1− a2q2 +1) (4”
HARDY-PETROVITCH-HUTCHINSON'S PROBLEM AND PARTIAL THETA FUNCTION (2011, background): “Suppose that the statement of the theorem is not true, and denote by j the smallest index such that δj 3, so that δj−1 ≥ 3 and δj 3 (j = 3, 4, . . . , n).”
Functional equations for Mahler measures of genus-one curves (2006, background): “Berndt proved virtually all of the necessary modular equations while editing Ramanujan’s notebooks, see [1], [4], [5], and [6].”
RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION (2010, background): “For introductions to the beautiful theory of the cubic continued fraction, see [ 7 , 13].”