Shintani zeta-functions and Gross – Stark units for totally real fields

@inproceedings{Dasgupta2007ShintaniZA,
  title={Shintani zeta-functions and Gross – Stark units for totally real fields},
  author={Samit Dasgupta},
  year={2007}
}
Let F be a totally real number field and let p be a finite prime of F , such that p splits completely in the finite abelian extension H of F . Stark has proposed a conjecture stating the existence of a p-unit in H with absolute values at the places above p specified in terms of the values at zero of the partial zeta-functions associated to H/F . Gross proposed a refinement of Stark’s conjecture which gives a conjectural formula for the image of Stark’s unit in F× p /Ê, where Fp denotes the… CONTINUE READING