On the order of lacunary sums of binomial coefficients.
On the order of magnitude of the difference between consecutive prime numbers
On the order of points on curves over finite fields.
On the order of the Mertens function.
On the order of unimodular matrices modulo integers
On the order of vanishing of modular -functions at the critical point
On the order of
On the order three Brauer classes for cubic surfaces
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over ℚ such that Br(S)/Br(ℚ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.
On the orders of zero of certain functions
On the ordinarity of the maximal real subfield of cyclotomic function fields
The aim of this paper is to clarify the ordinarity of cyclotomic function fields. In the previous work [J. Number Theory 133 (2013)], the author determined all monic irreducible polynomials m such that the maximal real subfield of the mth cyclotomic function field is ordinary. In this paper, we extend this result to the general case.
On the orthogonal groups of unimodular quadratic forms. II.
On the orthogonal symmetry of L-functions of a family of Hecke Grössencharacters
The family of symmetric powers of an L-function associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and p-adic points of view. Here we examine one explicit such family from the perspectives of classical analytic number theory and random matrix theory, especially focusing on evidence for the symmetry type of the family. In particular, we investigate the values at the central point and give evidence that this family can be modeled by...
On the -adic continuation of the logarithmic derivative of certain hypergeometric functions
On the adic nearby cycles of log smooth families
On the problem
On the packing densities of superballs and other bodies.
On the p-adic Eichler-Shimura isomorphism for ...-adic cusp forms.
On the p-adic height of Heegner cycles.
On the p-adic Leopoldt transform of a power series
On the p-adic Waring's problem