一般注記We study the distribution of Campana points of bounded height on biequivariant compactifications of the Heisenberg group, and prove the log Manin conjecture introduced by M. Pieropan, A. Smeets, S. Tanimoto and A. Varilly-Alvarado, on the asymptotic formula for the number of such Campana points.In Chapter 1 we review the notions of adelically metrized line bundles and heights on adelic spaces. They are basic for the height functions and height zeta functions associated to a given line bundle.In Chapter 2 we review the classical Manin's conjecture including its background, formulation, and various approaches and progress toward it.In Chapter 3 we recall the log Manin conjecture introduced by M. Pieropan, A. Smeets, S. Tanimoto and A. Varilly-Alvarado. The log Manin conjecture concerns the distribution of Campana points of bounded height on Fano Campana orbifolds over number fields. We review the background, the statement and the progress toward the log Manin conjecture.In Chapter 4 we review the theory of the Heisenberg group, especially its representation theory. We discuss the height zeta function associated with Campana points on biequivariant compactifications of the Heisenberg group.In Chapter 5 we prove the log Manin conjecture by the height zeta function method, for biequivaraint compactifications of the Heisenberg group over the field of rational numbers under mild conditions.
連携機関・データベース国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）