The abelian group E(Q) of rational points on E is finitely generated [Mor22]. Hence E(Q) ' Z ⊕ T for some nonnegative integer r (the rank) and some finite abelian group T (the torsion subgroup). The torsion subgroup is well understood, thanks to B. Mazur [Maz77], but the rank remains a mystery. Already in 1901, H. Poincaré [Poi01, p. 173] asked what is the range of possibilities for the minimum...

The Ugi reaction offers an effective method for preparing chromophore-appended DOTA-monoamide ligands, which can readily be elaborated to their lanthanide complexes.

Radionuclides are needed both for nuclear medicine imaging as well as for peptide-receptor radionuclide therapy (PRRT) of neuroendocrine tumors (NET). Imaging is important in the initial diagnostic work-up and for staging NETs. In therapy planning, somatostatin receptor imaging (SRI) is used when treatment is targeted at the somatostatin receptors as with the use of somatostatin analogues or PR...

Let E be an elliptic curve over Q and ` be an odd prime. Also, let K be a number field and assume that E has a semi-stable reduction at `. Under certain assumptions, we prove the vanishing of the Galois cohomology group H1(Gal(K(E[`i])/K), E[`i]) for all i ≥ 1. When K is an imaginary quadratic field with the usual Heegner assumption, this vanishing theorem enables us to extend a result of Kolyv...

We give an elementary proof of the Mazur-TateTeitelbaum conjecture for elliptic curves by using Kato’s element. 2000 Mathematics Subject Classification: 11F85, 11G05, 11G07, 11G40, 11S40.

In this paper, we study the relation between the cohomology of Coxeter groups and their parabolic subgroups of nite order. Let W be a Coxeter group and k a commutative ring with identity. We investigate the natural map : H (W; k) ! lim:inv: H (W F ; k), where W F runs all parabolic subgroups of nite order, and prove that the kernel and the cokernel of consist of nilpotent elements. This general...

The problem of estimating the number of imaginary quadratic fields whose ideal class group has an element of order ` ≥ 2 is classical in number theory. Analogous questions for quadratic twists of elliptic curves have been the focus of recent interest. Whereas works of Stewart and Top [St-T], and of Gouvêa and Mazur [G-M] address the nontriviality of MordellWeil groups, less is known about the n...