On Ramanujan's Q-function

Abstract : This study provides a detailed analysis of a function which Knuth discovered to play a central role in the analysis of hashing with linear probing. The function, named after Knuth Q(n), is related to several of Ramanujan's investigations. It surfaces in the analysis of a variety of algorithms ans discrete probability problems including hashing, the birthday paradox, random mapping statistics, the "rho" method for integer factorization, union-find algorithms, optimum caching, and the study of memory conflicts. A process related to the complex asymptotic methods of singularity analysis and saddle point integrals permits to precisely quantify the behaviour of the Q(n) function. in this way, tight bounds are derived. They answer a question of Knuth (the art of Computer Programming, vol. 1, 1968), itself a rephrasing of earlier questions of Ramanujan in 1911-1913.
Type de document :
[Research Report] RR-1760, INRIA. 1992
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Soumis le : lundi 29 mai 2006 - 11:48:49
Dernière modification le : vendredi 25 mai 2018 - 12:02:02
Document(s) archivé(s) le : vendredi 13 mai 2011 - 22:28:08



  • HAL Id : inria-00077000, version 1



Philippe Flajolet, P.J. Grabner, P. Kirschenhofer, H. Prodinger. On Ramanujan's Q-function. [Research Report] RR-1760, INRIA. 1992. 〈inria-00077000〉



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