Some debts I owe.
Some definite integrals associated with the Riemann zeta function.
Some Diophantine approximation results concerning linear recurrences
Some Diophantine equations of the form .
Some diophantine equations of the form
Some diophantine equations solvable by identities
Some diophantine equations with many solutions
Some distribution problems concerning the divisors of integers
Some Distribution Properties of 0,1-Sequences.
Some divisibility properties of binomial coefficients and the converse of Wolstenholme's theorem.
Some doubly exponential sums over ℤₘ
Some Effective Cases of the Brauer-Siegel Theorem.
Some elliptic function identities
Some estimates for diagonal equations over p-adic fields
Some estimates in the theory of Dedekind Zeta-functions
Some eta-identities arising from theta series.
Some euclidean properties for real quadratic fields
Some examples of 5 and 7 descent for elliptic curves over
We perform descent calculations for the families of elliptic curves over with a rational point of order or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and 7, and show that the 5-torsion of the Tate-Shafarevich group of an elliptic curve over may become arbitrarily large.
Some Examples of Weber-Hecke Ring Class Field Theory.
Some experimental results on the Frobenius problem.