On the Kodaira dimensions of Hilbert modular varieties.
We compute the -theory of -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the -theory of these semigroup -algebras in terms of the -theory for the reduced group -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.
The norm of a trigonometric polynomial with non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of
For an integer we denote by the largest prime factor of . We obtain several upper bounds on the number of solutions of congruences of the form and use these bounds to show that