arXiv subjects

Satoshi Wakatsuki

Publications and source records attributed to Satoshi Wakatsuki.

20 records · Page 2Linked to original sources

arXiv2013

On the geometric side of the Arthur trace formula for the symplectic group of rank 2

We study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group or the split symplectic group of rank 2 over any algebraic number field. In particular, we show that the coefficients of unipotent orbital integrals are expressed by the Dedekind zeta function, Hecke L-functions, and the Shintani zeta function for the space of binary quadratic forms.

math.NT↗

arXiv2007

On relations among Dirichlet series whose coefficients are class numbers of binary cubic forms

We study the class numbers of integral binary cubic forms. For each $SL_2(Z)$ invariant lattice $L$, Shintani introduced Dirichlet series whose coefficients are the class numbers of binary cubic forms in $L$. We classify the invariant lattices, and investigate explicit relationships between Dirichlet series associated with those lattices. We also study the analytic properties of the Dirichlet series, and rewrite the functional equation in a self dual form using the explicit relationship.

math.NT↗