Certain values of Hecke \(L\)-functions and generalized hypergeometric functions
For a smooth projective curve \(X\), one has the regular map from the motivic cohomology group of \(X\), which is given by Milnor \(K\)-groups, to the real Deligne cohomology group. The regular map is closely related to the Beilinson's conjecture on special values of \(L\)-functions of motives. Now let \(X\) be a Fermat curve of degree \(N\). For the cases \(N=3,4\), in this paper the author reformulates the regular maps (after Bloch) and then obtains the special values of \(L\)-functions at \(s=0\) for the Jacobi-sum Hecke characters of the \(N\)th cyclotomic fields over \(\mathbb Q\) by means of generalized hypergeometric functions, respectively.
scientific article; zbMATH DE number 5859971
scientific article