Page 1 Next

Displaying 1 – 20 of 173

Showing per page

A cubic analogue of the theta series.

Journal für die reine und angewandte Mathematik

A cubic analogue of the theta series. II.

Journal für die reine und angewandte Mathematik

Acta Arithmetica

A formula for the number of solutions of a restricted linear congruence

Mathematica Bohemica

Consider the linear congruence equation ${x}_{1}+...+{x}_{k}\equiv b\phantom{\rule{4.44443pt}{0ex}}\left(mod\phantom{\rule{0.277778em}{0ex}}{n}^{s}\right)$ for $b\in ℤ$, $n,s\in ℕ$. Let ${\left(a,b\right)}_{s}$ denote the generalized gcd of $a$ and $b$ which is the largest ${l}^{s}$ with $l\in ℕ$ dividing $a$ and $b$ simultaneously. Let ${d}_{1},...,{d}_{\tau \left(n\right)}$ be all positive divisors of $n$. For each ${d}_{j}\mid n$, define ${𝒞}_{j,s}\left(n\right)=\left\{1\le x\le {n}^{s}:{\left(x,{n}^{s}\right)}_{s}={d}_{j}^{s}\right\}$. K. Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on ${x}_{i}$. We generalize their result with generalized gcd restrictions on ${x}_{i}$ and prove that for the above linear congruence, the number of solutions...

Acta Arithmetica

Acta Arithmetica

A new method of estimation of trigonometrical sums.

Matematiceskij sbornik

A note on character sums over finite fields.

Journal für die reine und angewandte Mathematik

A note on exponential sums.

Mathematica Scandinavica

A note on the zeros of exponential polynomials

Compositio Mathematica

Acta Arithmetica

A trace formula for Jacobi forms.

Journal für die reine und angewandte Mathematik

Séminaire Delange-Pisot-Poitou. Théorie des nombres

An elementary treatment of a general diophantine problem

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

An example for Gelfand's theory of commutative Banach algebras

Mathematica Slovaca

Acta Arithmetica

Acta Arithmetica

Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.

Journal für die reine und angewandte Mathematik

Acta Arithmetica

Arithmetic progressions in sumsets

Acta Arithmetica

1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B always contains an arithmetic progression of length $exp{\left(logN\right)}^{1/3-\epsilon }$. Our aim is to show that this is not very far from the best possible. Theorem 1. Let ε be a positive number. For every prime p > p₀(ε) there is a symmetric set A of residues mod p such that |A| > (1/2-ε)p and A + A contains no arithmetic progression of length (1.1)$exp{\left(logp\right)}^{2/3+\epsilon }$. A set of residues can be used to get a set of integers in an obvious way. Observe...

Page 1 Next