For an odd prime p, we prove the p-part of the Birch and Swinnerton-Dyer formula for semistable elliptic curves of analytic rank one.

By applying the residue method for period integrals and Langlands-Shahidi’s theory for residues of Eisenstein series, we study the period integrals for six spherical varieties. For each spherical variety, we prove a relation between the period integrals and certain automorphic L-functions. In some cases, we also study the local multiplicity of the spherical varieties.

No abstract uploaded!

No abstract uploaded!

We give an example of a dominant rational self-map of the projective plane whose dynamical degree is a transcendental number.