منابع مشابه
Additive Functions on Shifted Primes
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes. A real-valued function / defined on the positive integers is additive if it satisfies f(rs) = f(r) + f(s) whenever r and s are coprime. Such functions are determined by their values on the prime-powers. For additive arithmetic function /, let Q denote the frequency...
متن کاملDivisors of Shifted Primes
Abstract. We bound from below the number of shifted primes p+s ≤ x that have a divisor in a given interval (y, z]. Kevin Ford has obtained upper bounds of the expected order of magnitude on this quantity as well as lower bounds in a special case of the parameters y and z. We supply here the corresponding lower bounds in a broad range of the parameters y and z. As expected, these bounds depend h...
متن کاملMultiple Recurrence and Convergence for Certain Averages along Shifted Primes
We show that any subset A ⊂ N with positive upper Banach density contains the pattern {m,m + [nα], . . . ,m + k[nα]}, for some m ∈ N and n = p − 1 for some prime p, where α ∈ R\Q. Making use for the Furstenberg Correspondence Principle, we do this by proving an associated recurrence result in ergodic theory along the shifted primes. We also prove the convergence result for the associated averag...
متن کاملThe Polynomial Multidimensional Szemerédi Theorem along Shifted Primes
If ~q1, . . . , ~qm : Z → Z are polynomials with zero constant terms and E ⊂ Z has positive upper Banach density, then we show that the set E ∩ (E − ~q1(p− 1))∩ . . .∩(E−~qm(p−1)) is nonempty for some prime p. We also prove mean convergence for the associated averages along the prime numbers, conditional to analogous convergence results along the full integers. This generalizes earlier results ...
متن کاملLaplacians on Shifted Multicomplexes
The Laplacian of an undirected graph is a square matrix, whose eigenvalues yield important information. We can regard graphs as one-dimensional simplicial complexes, and as whether there is a generalisation of the Laplacian operator to simplicial complexes. It turns out that there is, and that is useful for calculating real Betti numbers [8]. Duval and Reiner [5] have studied Laplacians of a sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1975
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-27-1-333-352