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### 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

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

### Adèles et séries trigonométriques spéciales

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  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...

Acta Arithmetica

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