On the conjecture of Lichtenbaum and of Chinburg over function fields.
On the conjectures of Birch and Swinnerton-Dyer and a geometric analog
On the conjectures of Mordell and Lang in positive characteristics.
On the Connected Part of the Covariant Tate p-divisible Group and the ?-function of the Family of Hyperelliptic Curves y2 = 1 + ? xN Modulo Various Primes.
On the Construction of Galois Extensions of Function Fields and Number Fields.
On the continued fractions of quadratic surds
On the Converse of Abel's Theorem in Characteristic p.
On the critical values of Hecke L-series
On the cuspidal divisor class group of a Drinfeld modular curve.
On the de Rham and -adic realizations of the elliptic polylogarithm for CM elliptic curves
In this paper, we give an explicit description of the de Rham and -adic polylogarithms for elliptic curves using the Kronecker theta function. In particular, consider an elliptic curve defined over an imaginary quadratic field with complex multiplication by the full ring of integers of . Note that our condition implies that has class number one. Assume in addition that has good reduction above a prime unramified in . In this case, we prove that the specializations of the -adic elliptic...
On the de Rham isomorphism for Drinfeld modules.
On the degree of a local zeta function
On the degree of the -function associated with an exponential sum
On the Difference of the Weil Height and the Néron-Tate Height.
On the Diophantine equation ... (X, Y) = ... (x, y).
On the discrete logarithm problem for plane curves
In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem for non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of , where is the cardinality of the ground field. Moreover, it is proven that for every fixed natural number the following holds: We consider the discrete logarithm problem for curves given by plane models...
On the distribution of rational points on certain Kummer surfaces
On the distribution of the Fₚ-points on an affine curve in r dimensions
On the divisibility properties of families of filtered F-crystals.
On the dual variety in characteristic 2