Sum of Square Roots of Polynomials and of Integers

by Dr Neeraj Kayal (Microsoft Research Lab., Bangalore)

Tuesday 19 Apr 2011, 14:30 → 15:30 Asia/Kolkata

A-212 (Colaba Campus)

Let a_1, a_2, ..., a_n and b_1, b_2, ..., b_n be positive integers each of which is at most n bits long. Let S be the difference between the sum of square roots of a_i's and the sum of square roots of the b_j's. If S is nonzero how small can it be in absolute value? It is conjectured that in absolute absolue value S must be at least 1/(2^{poly(n)}). In this talk we will see the solution of a polynomial analog of this conjecture.