Ch6(KawaharaTakemura)

We shall give a method for systematic computation of γ K , give some general upper and lower bounds, and study three special cases more closely, including that of curves with

The set of families K that we shall consider includes the family of real or imaginary quadratic fields, that of real biquadratic fields, the full cyclotomic fields, their maximal

In this expository paper, we illustrate two explicit methods which lead to special L-values of certain modular forms admitting complex multiplication (CM), motivated in part

In this section we look at spectral sequences for calculating the homology of the bar and cobar constructions on operads and cooperads in based spaces or spectra.. It turns out that

We present combinatorial proofs of several non-commutative extensions, and find a β-extension that is both a generalization of Sylvester’s identity and the β-extension of the

proof of uniqueness divides itself into two parts, the first of which is the determination of a limit solution whose integral difference from both given solutions may be estimated

When a 4-manifold has a non-zero Seiberg-Witten invariant, a Weitzenb¨ ock argument shows that it cannot admit metrics of positive scalar curvature; and as a consequence, there are

Such bounds are of interest because they can be used to improve estimates of volumes of hyperbolic manifolds in much the same way that B¨ or¨ oczky’s bounds [B¨ o1], [B¨ o2] for