  We introduce the notion of Shintani data, which axiomatizes algebraic aspects
of Shintani zeta functions. We develop the general theory of Shintani data, and
show that the order of vanishing part of Gross's conjecture follows from the
existence of a Shintani datum. Recently, Dasgupta and Spiess proved the order
of vanishing part of Gross's conjecture under certain conditions. We give an
alternative proof of their result by constructing a certain Shintani datum. We
also propose a refinement of Gross's leading term conjecture by using the
theory of Shintani data. Out conjecture gives a conjectural construction of
localized Rubin-Stark elements which can be regarded as a higher rank
generalization of the conjectural construction of Gross-Stark units due to
Dasgupta and Dasgupta-Spiess.
