On the Behaviour of p-Adic L-Functions at s= 0.
On the classgroups of imaginary abelian fields
Let be an odd prime, an odd, -adic Dirichlet character and the cyclic imaginary extension of associated to . We define a “-part” of the Sylow -subgroup of the class group of and prove a result relating its -divisibility to that of the generalized Bernoulli number . This uses the results of Mazur and Wiles in Iwasawa theory over . The more difficult case, in which divides the order of is our chief concern. In this case the result is new and confirms an earlier conjecture of G....
On the cyclicity of a Galois module in local fields.
On the cyclotomic invariants of Iwasawa.
On the Definition of Hilbert Space.
On the deformation of Artin-Schreier to Kummer
On the degree of a local zeta function
On the distribution of the -Euler polynomials and the -Genocchi polynomials of higher order.
On the Factorization of p-adic L-series.
On the Functional Equation of the Artin L-Function for Characters of Real Representations.
On the generalized Bernoulli numbers that belong to unequal characters.
The study of class number invariants of absolute abelian fields, the investigation of congruences for special values of L-functions, Fourier coefficients of half-integral weight modular forms, Rubin's congruences involving the special values of L-functions of elliptic curves with complex multiplication, and many other problems require congruence properties of the generalized Bernoulli numbers (see [16]-[18], [12], [29], [3], etc.). The first steps in this direction can be found in the papers of...
On the genus group of algebraic number fields
On the Győry-Sárközy-Stewart conjecture in function fields
We consider function field analogues of the conjecture of Győry, Sárközy and Stewart (1996) on the greatest prime divisor of the product for distinct positive integers , and . In particular, we show that, under some natural conditions on rational functions , the number of distinct zeros and poles of the shifted products and grows linearly with if . We also obtain a version of this result for rational functions over a finite field.
On the Hilbert symbol in cyclotomic fields
On the Homomorphisms of the Integral Linear Groups.
On the identities of symmetry for the generalized Bernoulli polynomials attached to of higher order.
On the identities of symmetry for the -Euler polynomials of higher order.
On the ?-invariant of the ?-transform of a rational function.
On the Iwasawa invariants of certain -extensions
On the jumps in the series of ramifications groups