A Theorem on Totally Mulitplicative Functions.
A theorem on triangular numbers
A third derivative test for mean values of exponential sums with application to lattice point problems
A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound.
A trace formula for Jacobi forms.
A trace formula for reductive groups. II : applications of a truncation operator
A trigonometrical identity.
A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations,...
A Turán-Kubilius type inequality on sum sets
A tutorial on conformal groups
Our concern is with the group of conformal transformations of a finite-dimensional real quadratic space of signature (p,q), that is one that is isomorphic to , the real vector space , furnished with the quadratic form , and especially with a description of this group that involves Clifford algebras.
A twisted class number formula and Gross's special units over an imaginary quadratic field
Let be a finite abelian extension of number fields with imaginary quadratic. Let be the ring of integers of and a rational integer. We construct a submodule in the higher odd-degree algebraic -groups of using corresponding Gross’s special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher “twisted” class number of , which is the cardinal of the finite algebraic -group .
A two-dimensional continued fraction algorithm for best approximations with an application in cubic number fields.
A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties
A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional continued...
A two-dimensional univoque set
Let J ⊂ ℝ² be the set of couples (x,q) with q > 1 such that x has at least one representation of the form with integer coefficients satisfying , i ≥ 1. In this case we say that is an expansion of x in base q. Let U be the set of couples (x,q) ∈ J such that x has exactly one expansion in base q. In this paper we deduce some topological and combinatorial properties of the set U. We characterize the closure of U, and we determine its Hausdorff dimension. For (x,q) ∈ J, we also prove new properties...
A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution
A two-sides omega-theorem for an asymmetric divisor problem.
A type of class group for imaginary quadratic fields
A Unified Theory of Proportion
A Unified Theory of Proportion
A uniform version of Jarník's theorem