A higher order p-adic class number formula

p-adic Verification of Class Number Computations

A p-ADIC WALDSPURGER FORMULA

In this article, we study p-adic torus periods for certain p-adic valued functions on Shimura curves coming from classical origin. We prove a p-adic Waldspurger formula for these periods, as a generalization of the recent work of Bertolini, Darmon, and Prasanna. In pursuing such a formula, we construct a new anti-cyclotomic p-adic L-function of Rankin– Selberg type. At a character of positive w...

ON p-ADIC WALDSPURGER FORMULA

conjugation, c, 5anti-cyclotomic p-adic L-function, L (π), 6Atkin–Serre operator, Θord, 13 canonical pairing, ( ,)A, 23convergent modular form, M(m,K), 14admissible, 15of finite tame level, M[ (m,K), 14stable, M[ (m,K)♥, 14universal, 15 distribution algebraA-related, D(A,K), 25ω-related, D(ω,K), 25π-related, D(π), 4 global Lubin–Tate different...

Higher Order Degenerate Hermite-Bernoulli Polynomials Arising from $p$-Adic Integrals on $mathbb{Z}_p$

Our principal interest in this paper is to study higher order degenerate Hermite-Bernoulli polynomials arising from multivariate $p$-adic invariant integrals on $mathbb{Z}_p$. We give interesting identities and properties of these polynomials that are derived using the generating functions and $p$-adic integral equations. Several familiar and new results are shown to follow as special cases. So...

p-ADIC CLASS INVARIANTS

We develop a new p-adic algorithm to compute the minimal polynomial of a class invariant. Our approach works for virtually any modular function yielding class invariants. The main algorithmic tool is modular polynomials, a concept which we generalize to functions of higher level.