On normal numbers and powers of algebraic numbers.
On normal numbers mod
It is proved that a real-valued function , where I is an interval contained in [0,1), is not of the form with |q(x)|=1 a.e. if I has dyadic endpoints. A relation of this result to the uniform distribution mod 2 is also shown.
On normal sets of numbers
On numbers containing each block infinitely often.
On numbers of type
On numbers with a unique representation by a binary quadratic form
On numerical semigroups.
On Obláth's problem.
On octahedral extensions of and quadratic -curves
We give a necessary condition for a surjective representation Gal to arise from the -torsion of a -curve. We pay a special attention to the case of quadratic -curves.
On octic fields of exponent 2.
On Optimal Extreme-Discrepancy Point Sets in the Square.
On ordinary ...-adic representations associated to modular forms.
On ordinary linear -adic differential equations with algebraic function coefficients
On orthogonal decomposition of homogeneous polynomials
On orthogonal polynomials related to Fibonacci numbers
On orthogonal systems and permutation polynomials in several variables
On oscillations in the additive divisor problem, 1
On -Ranks in the Class Field Tower Problem
Much recent progress in the 2-class field tower problem revolves around demonstrating infinite such towers for fields – in particular, quadratic fields – whose class groups have large 4-ranks. Generalizing to all primes, we use Golod-Safarevic-type inequalities to analyse the source of the -rank of the class group as a quantity of relevance in the -class field tower problem. We also make significant partial progress toward demonstrating that all real quadratic number fields whose class groups...
On -adic analogue of -Bernstein polynomials and related integrals.
On -adic analytic families of Galois representations