Linear independence result for p-adic L-values

Irrationality of some p-adic L-values

We give a proof of the irrationality of the p-adic zeta-values ζp(k) for p = 2, 3 and k = 2, 3. Such results were recently obtained by F.Calegari as an application of overconvergent p-adic modular forms. In this paper we present an approach using classical continued fractions discovered by Stieltjes. In addition we show irrationality of some other p-adic L-series values, and values of the p-adi...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

Abelian varieties, l-adic representations, and l-independence

In the case that K is a number field, this conjecture goes back almost thirty years. The Lie algebra analogue has been formulated by J. Tate [18], D. Mumford [10], and J.-P. Serre [13]. A more precise conjecture involves comparison with the singular homology group H1(A(C),Q) for a fixed embedding K ⊂ C. If G∞ denotes the associated Hodge group (cf. §4), the “Mumford-Tate” conjecture states that...

Multivariate P-adic L-function

In the recent, many mathematicians studied the multiple zeta function in the complex number field. In this paper we construct the p-adic analogue of multiple zeta function which interpolates the generalized multiple Bernoulli numbers attached to χ at negative integers. §1. Introduction Let p be a fixed prime. Throughout this paper Z p , Q p , C and C p will, respectively, denote the ring of p-a...

Twisted signs for p-adic linear groups

Let G be a reductive p-adic group and let θ be an automorphism of G of order at most two. Let π be an irreducible smooth representation of G that is taken to its dual by θ. The space V of π then carries a non-zero bilinear form ( , ) ( unique up to scaling) with the invariance property (π(g)v, π(g)w) = (v, w), for g ∈ G and v, w ∈ V . The form is easily seen to be symmetric or skew-symmetric an...