Quadratic forms, fibre products and some plane curves with many points
We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic-adic -functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic -adic -functions to more general Shimura curves.
For any non-square 1 < D ≡ 0,1 (mod 4), Zagier defined . Here we use the theory of periods to give identities and congruences which relate various values of .