A note on functional equations of the -adic polylogarithms
A note on generalized mobius ...-functions
A note on global units and local units of function fields
A note on Greenberg's cojecture for real abelian number fields.
A Note on heights in certain infinite extensions of
We study the behaviour of the absolute Weil height of algebraic numbers in certain infinite extensions of . In particular, we obtain a Northcott type property for infinite abelian extensions of finite exponent and also a Bogomolov type property for certain fields which are a -adic analog of totally real fields. Moreover, we obtain a non-archimedean analog of a uniform distribution theorem of Bilu in the archimedean case.
A note on integral clock triangles.
A note on integral points on elliptic curves
We investigate a problem considered by Zagier and Elkies, of finding large integral points on elliptic curves. By writing down a generic polynomial solution and equating coefficients, we are led to suspect four extremal cases that still might have nondegenerate solutions. Each of these cases gives rise to a polynomial system of equations, the first being solved by Elkies in 1988 using the resultant methods of Macsyma, with there being a unique rational nondegenerate solution. For the second case...
A note on involutory automorphisms of and the use of algebraically independent numbers for the construction of diagonable matrices
A note on irregularities in distribution of sequences of integers
A note on Jeśmanowicz' conjecture
A note on Jeśmanowicz' conjecture concerning primitive Pythagorean triplets
A note on Krawtchouk polynomials and Riordan arrays.
A note on lacunary lonely runners. WITHDRAWN.
A note on large gaps between consecutive prime numbers
A note on large gaps between prime numbers
A note on linear preserves of ternary cubic forms
A note on linear recurrent Mahler numbers.
A Note on Link Complements and Arithmetic Groups.
A note on minimal zero-sum sequences over ℤ
A zero-sum sequence over ℤ is a sequence with terms in ℤ that sum to 0. It is called minimal if it does not contain a proper zero-sum subsequence. Consider a minimal zero-sum sequence over ℤ with positive terms and negative terms . We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where . These bounds are tight and improve upon previous results. We also show a natural partial order structure on the collection of all minimal zero-sum sequences over the set i∈ ℤ : -n ≤ i ≤ n for any positive integer n.
A Note on Moments of Zeta'(1/2+i Gamma)