Related papers: On Weyl sums over primes in short intervals

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes. The latter have applications to…

Definition of the number of prime numbers in the given interval

We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…

In this work we derive results concerning Elliptic Functions using as tools general formulas from previus work.

We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.

In this paper, we prove certain theorems about three consecutive primes.

We obtain a lower bound for a number of primes in tuples. As applications, we obtain a lower bound for the Romanoff type representation functions.

This paper introduces a general technique for estimating the absolute value of pure Gaussian sums of order k over a prime p for a class of composite order k. The new estimate improves the classical estimate by a factor of about 2 or better…

In this paper we study the mean values of some multiplicative functions connected with the divisor function on the short interval of summation. The asymptocic values for such mean values are proved.

We determine the behavior of multiplicative functions vanishing at a positive proportion of prime numbers in almost all short intervals. Furthermore we quantify "almost all" with uniform power-saving upper bounds, that is, we save a power…

In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.

In this paper, we provide formulas for partial sums of weighted averages over regular integers modulo $n$ of the $\gcd$-sum function with any arithmetic function. Many interesting applications of the results are also given.

Using evaluations of the difference between consecutive primes we develop another way of estimating of the number of primes in the interval $(n, 2n)$. We also discuss the ultra Cramer conjecture, $p_{n+1} - p_n = O(log^{1+\epsilon}p_n)$…

We prove a general estimate for the Weyl remainder of an elliptic, semiclassical pseudodifferential operator in terms of volumes of recurrence sets for the Hamilton flow of its principal symbol. This quantifies earlier results of Volovoy.…

We study in an explicit manner the partial sums of the multiplicative inverse of the Riemann zeta function and its derivative.

Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.

This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the…

In this paper, we study the weighted sums of multiple t-values and of multiple t-star values at even arguments. Some general weighted sum formulas are given, where the weight coefficients are given by (symmetric) polynomials of the…