Add to ORKGThe present note is an essential addition to the author's arxiv paper arXiv:2001.01070, concerning general multiplicative systems of random variables. Using some lemmas and the methodology of \cite{Kar4}, we obtain a general extreme inequality, with corollaries involving Rademacher chaos sums and those analogues for multiplicative systems. In particular we prove that a system of functions generated by bounded products of a multiplicative system is a convergence system.Comment: The present note is an essential addition to the author's arxiv paper arXiv:2001.0107
We determine the order of magnitude of E|∑n≤xf(n)|2q, where f(n) is a Steinhaus or Rademacher random...
We determine the order of magnitude of E|∑n≤xf(n)|2q, where f(n) is a Steinhaus or Rademacher random...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
We prove a pointwise convergence result for additive ergodic averages associated with certain multip...
Resolving a conjecture of Helson, Harper recently established that partial sums of random multiplica...
We prove that $\log n$ is an almost everywhere convergence Weyl multiplier for the orthonormal syste...
Abstract A completely elementary and self-contained proof of convergence of Gaussian multiplicative ...
We establish a normal approximation for the limiting distribution of partial sums of random Rademach...
We obtain a condition for the Lq-convergence of martingales generated by random multiplicative casca...
A Steinhaus random multiplicative function $f$ is a completely multiplicative function obtained by s...
International audienceLet P denote the set of primes and {f (p)} p∈P be a sequence of independent Be...
We prove that if f(n) is a Steinhaus or Rademacher random multiplicative function, there almost sure...
In this note we are interested in cancellations in sums of multiplicative functions. It is well know...
In this note we are interested in cancellations in sums of multiplicative functions. It is well know...
We consider powers of the absolute value of the characteristic polynomial of Haar distributed random...
We determine the order of magnitude of E|∑n≤xf(n)|2q, where f(n) is a Steinhaus or Rademacher random...
We determine the order of magnitude of E|∑n≤xf(n)|2q, where f(n) is a Steinhaus or Rademacher random...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
We prove a pointwise convergence result for additive ergodic averages associated with certain multip...
Resolving a conjecture of Helson, Harper recently established that partial sums of random multiplica...
We prove that $\log n$ is an almost everywhere convergence Weyl multiplier for the orthonormal syste...
Abstract A completely elementary and self-contained proof of convergence of Gaussian multiplicative ...
We establish a normal approximation for the limiting distribution of partial sums of random Rademach...
We obtain a condition for the Lq-convergence of martingales generated by random multiplicative casca...
A Steinhaus random multiplicative function $f$ is a completely multiplicative function obtained by s...
International audienceLet P denote the set of primes and {f (p)} p∈P be a sequence of independent Be...
We prove that if f(n) is a Steinhaus or Rademacher random multiplicative function, there almost sure...
In this note we are interested in cancellations in sums of multiplicative functions. It is well know...
In this note we are interested in cancellations in sums of multiplicative functions. It is well know...
We consider powers of the absolute value of the characteristic polynomial of Haar distributed random...
We determine the order of magnitude of E|∑n≤xf(n)|2q, where f(n) is a Steinhaus or Rademacher random...
We determine the order of magnitude of E|∑n≤xf(n)|2q, where f(n) is a Steinhaus or Rademacher random...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...