School of Physical Sciences
Jawaharlal Nehru University, New Delhi
Title : A generalization of the 3d distance theorem
Speaker: Manish Mishra (IISER, Pune)
Date: Feb– 11 -2020
Time: 4.00 pm, Tuesday
Venue: Seminar Room, SPS
Abstract : Let P be a positive rational number. Call a function f : R → R to have finite gaps property mod P if the following holds: for any positive irrational α and positive integer M, when the values of f(mα), 1 ≤ m ≤ M, are inserted mod P into the interval [0,P) and arranged in increasing order, the number of distinct gaps between successive terms is bounded by a constant kf which depends only on f. In this note, we prove a generalization of the 3d distance theorem of Chung and Graham. As a consequence, we show that a piecewise linear map with rational slopes and having only finitely many non- differentiable points has finite gaps property mod P. We also show that if f is distance to the nearest integer function, then it has finite gaps property mod 1with kf ≤ 6. This is a joint work with Amy Philip.