Yasutaka Ihara

Profinite braid groups, Galois representations and complex multiplications

In this paper, we consider two closely correlated subjects. One is a pro-i analogue of the braid group, and the other is a construction of the universal 1-adic power series for complex multiplications of Fermat type, or equivalently, for Jacobi sums. Both arise from, and constitute, a first step in the study of the canonical representation of the absolute Galois group GQ = Gal(Q/Q) in the outer automorphism group of the profinite fundamental group of PQ \{O,1,oo}.

On the Euler-Kronecker constants of global fields and primes with small norms

Let K be a global field, i.e., either an algebraic number field of finite degree (abbreviated NF), or an algebraic function field of one variable over a finite field (FF). Let ζK(s) be the Dedekind zeta function of K, with the Laurent expansion at s = 1:

On the stable derivation algebra associated with some braid groups

\zeta _K \left( s \right) = c_{ - 1} \left( {s - 1} \right)^{ - 1} + c_0 + c_1 \left( {s - 1} \right) + \cdots \left( {c_{ - 1} \ne 0} \right)

On Automorphic Forms on the Unitary Symplectic Group Sp (n) and SL2 (R).

(0.1) In this paper, we shall present a systematic study of the real number

On the Value-Distribution of Logarithmic Derivatives of Dirichlet L -Functions

\gamma _K = {{c_0 } \mathord{\left/ {\vphantom {{c_0 } {c_{ - 1} }}} \right. \kern-\nulldelimiterspace} {c_{ - 1} }}

On Certain Arithmetic Functions M (s; z1; z2) Associated with Global Fields: Analytic Properties

(0.2) attached to each K, which we call the Euler-Kronecker constant (or invariant) of K. When K = ℚ (the rational number field), it is nothing but the Euler-Mascheroni constant