Hall 123

Analytic properties of the multiple zeta functions and its variants

Biswajyoti Saha

IMSc

In the past couple of decades, the problem of analytic
continuation and determining the set of singularities of the multiple zeta
functions has been treated extensively by several mathematicians,
employing different methods. These methods then have been extended to
address similar problem in case of many other generalizations of the
multiple zeta functions, like the multiple Hurwitz zeta functions. The
analytic continuation have been achieved but the exact set of
singularities are known in very few cases. In this talk, we discuss the
method of translation and consider the multiple Lerch zeta functions which
unifies quite a few generalizations of the multiple zeta functions at the
same time. Using this method it is possible to determine the exact set of
singularities in some special cases. Our method is inspired by a
translation formula for the Riemann zeta function due to Ramanujan.