go The next installment in this series is eagerly awaited. This is the first step It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete.
More Books by George E. Berndt See All. Number Theory.
Lattice Path Combinatorics and Applications. Ramanujan's Lost Notebook. Wilson started on the project of editing Ramanujan's notebooks. However, Wilson died in and Watson seems to have lost interest in the project in the late s.
Whittaker examined Watson's papers which were a complete mess, due to be incinerated in a few days and found Ramanujan's notebook, which he and R. Rankin sent to Trinity College Wren library on December 26, It was published on December 22, , by Narosa publishing house.
George Andrews, an American mathematician, wrote in an account of the discovery for the th celebration of Ramanujan's birth. In , anticipating a sabbatical , he wrote to British mathematician Lucy Slater.
Slater "intriguingly" stated in her reply that she had inherited a "great collection" of papers from mathematicians such as Watson, Bailey, Jackson and Rogers, which were unsorted, including one of the last by Ramanujan. She also mentioned other papers were held by the Trinity College library. Although unable to travel to Europe in , Andrews became able to do so in , when he was due to attend a European conference in Strasbourg , near the France - Germany border.
Ramanujan's lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year. notebooks  to name this manuscript Ramanujan's lost notebook. Almost surely, this manuscript, or at least most of it, was written during the.
He obtained permission and support from Slater, from the Trinity College library, and from his professor, Ben Noble, to visit Cambridge after the conference, in order to investigate the "invaluable" unpublished writings of Watson et al. Noble agreed, adding that if he could attempt to find a lost paper by James Clerk Maxwell at the same time, it would be appreciated. The library's documents included a list of matters held from Watson's estate.
The list included the item: "A page manuscript by S. Ramanujan on q-series" , containing the work from Ramanujan's final year. Although not labelled as such, the identity of the papers was settled because Ramanujan's final letters to Hardy had referred to the discovery of what Ramanujan called mock theta functions, although without great detail, and the manuscript included what appeared to be his full notes on these.
Rankin described the lost notebook in detail. The majority of the formulas are about q -series and mock theta functions , about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series , congruences, and asymptotics.
The mock theta functions in the notebook have been found to be useful for calculating the entropy of black holes.
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