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
On -adic Euler constants
The goal of this article is to associate a -adic analytic function to the Euler constants , study the properties of these functions in the neighborhood of and introduce a -adic analogue of the infinite sum for an algebraic valued, periodic function . After this, we prove the theorem of Baker, Birch and Wirsing in this setup and discuss irrationality results associated to -adic Euler constants generalising the earlier known results in this direction. Finally, we define and prove certain...
On -adic geometric representations of .
On -adic -functions
On -adic -functions and the Riemann-Hurwitz genus formula
On -adic -functions of over totally real fields
Let be the Rankin product -function for two Hilbert cusp forms and . This -function is in fact the standard -function of an automorphic representation of the algebraic group defined over a totally real field. Under the ordinarity assumption at a given prime for and , we shall construct a -adic analytic function of several variables which interpolates the algebraic part of for critical integers , regarding all the ingredients , and as variables.