分野別セミナー

The complex n-th polygamma function is (n+1)-th derivative of the logarithm of the gamma function. In this talk I give a definition of p-adic polygamma functions which are continuous functions on Z_p, and characterized by certain linear combinations of overconvergent polylog functions. Ours are entirely different from Diamond's p-adic polygamma functions. Several formulas follows from well-known formulas on polylog. As an application I will show that our polygamma appears in syntomic regulators of K_2 of hypergeometric curves (actually this is the origin of our construction of p-adic polygamma).