A Note on the Voronoi Summation Formula.
A note on the weighted Khintchine-Groshev Theorem
Let denote the set of –approximable points in . The classical Khintchine–Groshev theorem assumes a monotonicity condition on the approximating functions . Removing monotonicity from the Khintchine–Groshev theorem is attributed to different authors for different cases of and . It can not be removed for as Duffin–Schaeffer provided the counter example. We deal with the only remaining case and thereby remove all unnecessary conditions from the Khintchine–Groshev theorem.
A note on the zeros of exponential polynomials
A note on the zeros of the derivative of the Riemann zeta function near the critical line
A Note on Thue's Equation Over Function Fields.
A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
In this note, we prove that there is no transcendental entire function such that and , for all sufficiently large , where .
A note on trilinear forms for reducible representations and Beilinson's conjectures
We extend Prasad’s results on the existence of trilinear forms on representations of of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomology of the product of two modular curves constructed by Beilinson.
A note on two conjectures
A note on two linear forms
We prove a result on approximations to a real number θ by algebraic numbers of degree ≤ 2 in the case when we have certain information about the uniform Diophantine exponent ω̂ for the linear form x₀ + θx₁ + θ²x₂.
A note on uniform or Banach density
In this note we present and comment three equivalent definitions of the so called uniform or Banach density of a set of positive integers.
A note on universal Hilbert sets.
A note on univoque self-sturmian numbers
We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic sturmian sequences. As a corollary to our study we obtain that a real number in is univoque and self-sturmian if and only if the -expansion of is of the form , where is a characteristic...
A note on univoque self-Sturmian numbers
We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number β in (1,2) is univoque and self-Sturmian if and only if the β-expansion of 1 is of the form 1v, where v is a characteristic...
A note on Waring's number modulo .
A note on Waring's problem in finite fields
A note on Waring's problem in GF (p)
A note on Waring's problem in p-adic fields
A note on weight enumerators of linear self-dual codes.
A note on zero-one laws in metrical Diophantine approximation
A note on zeta-functions of algebraic number fields