Thursday, July 9 2015
10:00 - 12:30

#### In 1731, Euler introduced the constant$\gamma:=\lim_{x\to \infty}(\sum_{n\le x}\frac{1}{n} - \log x}$while studying harmonic sums. This constant is known as Euler'sconstant. He computed $\gamma$ upto five decimal places and wroteit in terms of a conditionally convergent series involving zetavalues. Till today the arithmetic nature of this constant is notknown. Lehmer and Briggs independently studied this constant forarithmetic progressions to unravel the mystery around it. In 2008,Diamond and Ford generalised the constant over the finite sets ofprimes and linked it to the Riemann hypothesis. In 2014, in a workwith S. Gun and S.B. Sinha, we considered the generalised Euler'sconstant in arithmetic progressions and showed that in the infinitelist at most one number can be algebraic. In this talk we explore arecent work with S. Gun and V.K. Murty where we study the nature ofthese constants in more detail and establish linear independenceresults about them.

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