A problem in diophantine approximation found in Ramanujan's lost notebook

Bruce C. Berndt; Sun Kim

doi:10.1007/s11139-012-9404-8

A problem in diophantine approximation found in Ramanujan's lost notebook

Bruce C. Berndt
, Sun Kim^*

^*Corresponding author for this work

Department of Mathematics

University of Illinois at Urbana-Champaign
Ohio State University

Research output: Contribution to journal › Journal article › peer-review

Abstract

Pages 262-265 in Ramanujan's Lost Notebook and Other Unpublished Papers are devoted to a draft of a manuscript on an unusual problem in diophantine approximation. Ramanujan finds the maximum value of a polynomial when the variable takes rational values, and he observes the maxima's periodicity. Because definitions and theorems in the manuscript are imprecise, the authors have attempted to interpret Ramanujan's ideas and provide rigorous proofs.

Original language	English
Pages (from-to)	83-95
Number of pages	13
Journal	Ramanujan Journal
Volume	31
Issue number	1-2
DOIs	https://doi.org/10.1007/s11139-012-9404-8
State	Published - 2013.06

Keywords

Diophantine approximation
Greatest integer function
Ramanujan's lost notebook

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10.1007/s11139-012-9404-8

Cite this

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title = "A problem in diophantine approximation found in Ramanujan's lost notebook",

abstract = "Pages 262-265 in Ramanujan's Lost Notebook and Other Unpublished Papers are devoted to a draft of a manuscript on an unusual problem in diophantine approximation. Ramanujan finds the maximum value of a polynomial when the variable takes rational values, and he observes the maxima's periodicity. Because definitions and theorems in the manuscript are imprecise, the authors have attempted to interpret Ramanujan's ideas and provide rigorous proofs.",

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AB - Pages 262-265 in Ramanujan's Lost Notebook and Other Unpublished Papers are devoted to a draft of a manuscript on an unusual problem in diophantine approximation. Ramanujan finds the maximum value of a polynomial when the variable takes rational values, and he observes the maxima's periodicity. Because definitions and theorems in the manuscript are imprecise, the authors have attempted to interpret Ramanujan's ideas and provide rigorous proofs.

KW - Diophantine approximation

KW - Greatest integer function

KW - Ramanujan's lost notebook

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DO - 10.1007/s11139-012-9404-8

M3 - Journal article

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ER -

A problem in diophantine approximation found in Ramanujan's lost notebook

Abstract

Keywords

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