| Details: |
Abstract: The arithmetic nature of the Euler’s constant is one of the biggest unsolved problems in number
theory for almost three centuries. In an attempt to give a partial answer to the arithmetic nature of the Euler’s constant,
M Ram Murty and N. Saradha made a conjecture on linear independence of digamma values. In particular, they
conjectured that for any positive integer q > 1 and a field K over which the q -th cyclotomic polynomial is
irreducible, the co-prime digamma values are linearly independent over the field K. Further, they established
a connection between the arithmetic nature of the Euler’s constant to the above conjecture. In the first half of the talk, we will
first prove that the conjecture is true with at most one exceptional q. Later on we also make some remarks on
the linear independence of these digamma values with the arithmetic nature of the Euler’s constant. In the second half, we will
discuss some transcendence results related to some q-analogues of the Euler's constant. |