相关论文: Applications of some exponential sums on prime pow…

We continue our recent work on averages for ternary additive problems with powers of prime numbers.

This is a survey of old and new problems and results in additive number theory.

Research on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) Number Theory in recent years. In this survey, we present the key tools…

We extend some methods of bounding exponential sums of the type $\displaystyle\sum_{n\le N}e^{2\pi iag^n/p}$ to deal with the case when $g$ is not necessarily a primitive root. We also show some recent results of Shkredov concerning…

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

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…

The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…

This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.

The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…

Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.

We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give…

In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.

Improving and extending recent results of the author, we conditionally estimate exponential sums with Dirichlet coefficients of L-functions, both over all integers and over all primes in an interval. In particular, we establish new…

Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.

We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interval, whose admissible length depends on whether or not we…

In this paper we extend and improve all the previous results known in literature about weighted average, with Ces\`aro weight, of representations of an integer as sum of a positive arbitrary number of prime powers and a non-negative…

Certain new inequalities for the sums of factorials are presented.

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…

This is a survey article outlining what is known about absolute primes.

This paper gives new explicit formulas for sums of powers of integers and their reciprocals.