The Lang–Trotter conjecture for products of non-CM elliptic curves

The Ramanujan Journal - Inspired by the work of Lang–Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over $${\mathbb {Q}}$$ and by the subsequent...     

An Approach to Paracyclophane-Based Tetrathiafulvalenes: Synthesis and Characterization of a Pseudo-Geminal [2.2]Paracyclophane 1,3-Dithia-2-Thione

The synthesis of paracyclophane-based tetrathiafulvalene precursors is described in the context of the importance of these compounds in the field of material chemistry. Pseudo-geminal bis(1,3-dithia-2-thione) was synthesized via the corresponding 1,3-dithiol-2-ylium salt. The latter was obtained by a synthetic procedure that involves 4,15-bis(acetyl)[2.2]paracyclophane, a new compound of interest for many researchers.     

Intramolecular,Interrupted Homo-Nazarov Cascade Biscyclizations to Angular (Hetero)Aryl-Fused Polycycles

Herein, a SnCl₄-catalyzed intramolecular, interrupted homo-Nazarov cascade biscyclization to access angular (hetero)aryl-fused polycycles is reported. Subsequent decarboxylation of the readily enolizable products afforded the angular products in up to 71 % yield over two steps, with the trans-diastereomers as the major products. The cyclopropyl homo-Nazarov cyclization precursors were formed using a scalable and modular synthetic route that, ultimately, offers access to 6,6,6-, 6,6,5-, 6,5,6-, 6,6,5,6-, and 6,6,6,5-fused angular polycyclic products. To showcase the rigor and utility of the method, an 8-step total synthesis of (±)-1-oxoferruginol, an antibacterial aromatic abietane diterpenoid, was disclosed.     

Dirhodium(II) Carboxylate Catalyzed Formation of 1,2,3‐Trisubstituted Indoles from Styryl Azides

Dirhodium(II)‐carboxylate complexes were discovered to promote the selective migration of acyl groups in trisubstituted styryl azides to form 1,2,3‐trisubstituted indoles. The styryl azides are readily available in three steps from cyclobutanone and 2‐iodoaniline.