PROBLEM: Rational Shifts of Transcendental Functions

INVESTIGATOR: Tudor Dimofte

DESCRIPTION: Many continued fractions are almost periodic, where instead of having k digits repeat,
we have a block of length k, with each entry a linear function of the block number; we call these Linearly
Periodic numbers. For several interesting numbers x, the continued fraction expansions of x + p/q are
calculated, and an analysis of the dependence of the block length and functions on p/q is performed.

PAPERS: tdJP.dvi   tdJP.tex   tdJP.pdf

FIGURES: rless1.eps   rless2.eps   rless5acc.eps   rmore5.eps

PROGRAMS: JP1-rless.nb   Tan[1] 1.nb   tdJPdata1.xls

INVESTIGATORS: Dustin Steinhauer  and  Randy Qian

DESCRIPTION: We will look computationally for simple rational factor relationships between Mahler measures of specific polynomials and L-functions using techniques involving the LLL basis reduction algorithm. We will also look for rational
relationships between zeta(2n+1) and an experimentally postulated, rapidly converging formula which is of significant
interest to us.

PAPERS:   dr_jp.tex   dr_jp.dvi

PROGRAMS:  FinalContours.nb   LLLzeta(s).nb   CFchecker1.nb   approxformzeta(s).nb   approxformLfns.nb