Integral points for multi-norm tori

Omega Polynomial in Polybenzene Multi Tori

The polybenzene units BTX 48, X=A (armchair) and X=Z (zig-zag) dimerize forming “eclipsed” isomers, the oligomers of which form structures of five-fold symmetry, called multi-tori. Multi-tori can be designed by appropriate map operations. The genus of multi-tori was calculated from the number of tetrapodal units they consist. A description, in terms of Omega polynomial, of the two linearly peri...

Incompressibility of Generic Torsors of Norm Tori

Let p be a prime integer, F a field of characteristic not p, T the norm torus of a degree p extension field of F , and E a T -torsor over F such that the degree of each closed point on E is divisible by p (a generic T -torsor has this property). We prove that E is p-incompressible. Moreover, all smooth compactifications of E (including those given by toric varieties) are p-incompressible. The m...

Integral Points for Drinfeld Modules

We prove that in the backward orbit of a nonpreperiodic (nontorsion) point under the action of a Drinfeld module of generic characteristic there exist at most finitely many points S-integral with respect to another nonpreperiodic point. This provides the answer (in positive characteristic) to a question raised by Sookdeo in [26]. We also prove that for each nontorsion point z there exist at mos...

Weighted norm inequalities for singular integral operators

Weighted norm inequalities for integral transforms

Weighted (L, L) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the condit...