5 papers
Around a question of Baker
Neelam Kandhil, Purusottam Rath
For any positive integer , it is a question of Baker whether the numbers , where runs over the non-trivial characters mod , are linearly independent over $\mathb…
On two problems of Hardy and Mahler
Patrice Philippon, Purusottam Rath
It is a classical result of Mahler that for any rational number > 1 which is not an integer and any real 0 < c < 1, the set of positive integers n such that n < c n is nece…
Transcendental sums related to the zeros of zeta functions
Sanoli Gun, M. Ram Murty, Purusottam Rath
While the distribution of the non-trivial zeros of the Riemann zeta function constitutes a central theme in Mathematics, nothing is known about the algebraic nature of these non-tr…
A number field extension of a question of Milnor
Tapas Chatterjee, Sanoli Gun, Purusottam Rath
Milnor formulated a conjecture about rational linear independence of some special Hurwitz zeta values. The second and third authors along with Ram Murty studied this conjecture and…
Rational points on analytic varieties
Alexey Beshenov, Margaret Bilu, Yuri Bilu +1
These are expanded notes of the mini-courses on Pila's work that Yuri Bilu gave in Basel in April 2011, Yaroslavl in August 2011 and Chennai in February 2012. The topics covered in…