Results 21 to 30 of about 359 (44)

Abel Summation of Ramanujan-Fourier Series [PDF]

, 2015
Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions.
Washburn, John
core  

Diophantine approximation on lines with prime constraints

, 2013
We study the problem of Diophantine approximation on lines in R^2 with prime numerator and denominator.Comment: 14 ...
Baier, Stephan, Ghosh, Anish
core   +1 more source

Restricted simultaneous Diophantine approximation

, 2016
We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.Comment: 16 pages.
Baier, Stephan, Ghosh, Anish
core   +1 more source

Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences

Open Mathematics
The Piatetski-Shapiro sequences are sequences of the form (⌊nc⌋)n=1∞{\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers (⌊αn+β⌋)n=1∞{(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty }.
Qi Jinyun, Guo Victor Zhenyu
doaj   +1 more source

Note on sums involving the Euler function

, 2018
In this note, we provide refined estimates of the following sums involving the Euler totient function: $$\sum_{n\le x} \phi\left(\left[\frac{x}{n}\right]\right) \qquad \text{and} \qquad \sum_{n\le x} \frac{\phi([x/n])}{[x/n]}$$ where $[x]$ denotes the ...
Chern, Shane
core   +1 more source

Exponential sums with automatic sequences

, 2017
We show that automatic sequences are asymptotically orthogonal to periodic exponentials of type $e_q(f(n))$, where $f$ is a rational fraction, in the P\'olya-Vinogradov range.
Drappeau, Sary, Müllner, Clemens
core   +3 more sources

On Bilinear Exponential and Character Sums with Reciprocals of Polynomials

, 2015
We give nontrivial bounds for the bilinear sums $$ \sum_{u = 1}^{U} \sum_{v=1}^V \alpha_u \beta_v \mathbf{\,e}_p(u/f(v)) $$ where $\mathbf{\,e}_p(z)$ is a nontrivial additive character of the prime finite field ${\mathbb F}_p$ of $p$ elements, with ...
Shparlinski, Igor E.
core   +1 more source

On Weyl sums for smaller exponents [PDF]

, 2010
We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov's mean value theorem, and derive estimates of utility for exponents k of intermediate ...
D. Wooley, Kent D. Boklan, Trevor
core  

On the Distribution of Values and Zeros of Polynomial Systems over Arbitrary Sets

, 2012
Let $G_1,..., G_n \in \Fp[X_1,...,X_m]$ be $n$ polynomials in $m$ variables over the finite field $\Fp$ of $p$ elements. A result of {\'E}. Fouvry and N. M.
Kerr, Bryce, Shparlinski, Igor E.
core   +1 more source

The large sieve with sparse sets of moduli

, 2005
Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then apply our result to the case when S consists of sqares.
Baier, Stephan
core   +2 more sources