相关论文: Additive functions on shifted primes
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
A survey paper on some recent results on additive problems with prime powers.
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…
We establish sharp upper bounds on shifted moments of quadratic Dirichlet $L$-functions over function fields. As an application, we prove some bounds for moments of quadratic Dirichlet character sums over function fields.
We establish upper bounds for shifted moments of modular $L$-functions to a fixed prime level under the generalized Riemann hypothesis.
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet $L$-functions to a fixed modulus over function fields. We apply the result to obtain upper bounds on moments of Dirichlet character sums over…
Shifted convolution sums play a prominent r\^ole in analytic number theory. We investigate pointwise bounds, mean-square bounds, and average bounds for shifted convolution sums for Hecke eigenforms.
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…
The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic…
In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.
We study the simultaneous concentration of the values of several additive functions along polynomial shifts. Under a slight restriction, this yields an extension of a result from Hal\'asz in 1975.
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
We study the concentration of the distribution of an additive function, when the sequence of prime values of $f$ decays fast and has good spacing properties. In particular, we prove a conjecture by Erdos and Katai on the concentration of…
We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.
We demonstrate a simple analytic argument that may be used to bound the Levy concentration function of a sum of independent random variables. The main application is a version of a recent inequality due to Rudelson and Vershynin, and its…
We continue our recent work on averages for ternary additive problems with powers of prime numbers.
In the paper, some lower bounds for polygamma functions are refined.
In this note, an upper bound for the sum of fractional parts of certain smooth functions is established. Such sums arise naturally in numerous problems of analytic number theory. The main feature is here an improvement of the main term due…