Mass formula for supersingular abelian varieties of dimension three, a research announcement (Algebraic Number Theory and Related Topics 2014)

"Algebraic Number Theory and Related Topics 2014". December 1～5, 2014. edited by Takeshi Tsuji, Hiroki Takahashi and Yuichiro Hoshi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The Eichler-Deuring mass formula says that the weighted number of isomorphism classes of supersingular elliptic curves over an algebraically closed field of characteristic p is expressed as a simple polynomial in p. In 2009, C.-F. Yu and J.-D. Yu generalized this formula for supersingular abelian surfaces. In this paper, we show a mass formula for supersingular abelian three-folds of a-number equal to two. This is a short version of [11]