A cubic analogue of the theta series.
A cubic analogue of the theta series. II.
A discrete Fourier kernel and Fraenkel's tiling conjecture
A formula for the number of solutions of a restricted linear congruence
Consider the linear congruence equation for , . Let denote the generalized gcd of and which is the largest with dividing and simultaneously. Let be all positive divisors of . For each , define . 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 . We generalize their result with generalized gcd restrictions on and prove that for the above linear congruence, the number of solutions...
A further refinement of Mordell's bound on exponential sums
A general discrepancy estimate based on p-adic arithmetics
A new method of estimation of trigonometrical sums.
A note on character sums over finite fields.
A note on exponential sums.
A note on the zeros of exponential polynomials
A notion of diaphony based on p-adic arithmetic
A trace formula for Jacobi forms.
Adèles et séries trigonométriques spéciales
An elementary treatment of a general diophantine problem
An example for Gelfand's theory of commutative Banach algebras
An exponential polynomial formed with the Legendre symbol
An improvement on Olson's constant for ℤₚ ⊕ ℤₚ
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Arcs with no more than two integer points on conics
Arithmetic progressions in sumsets
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 . 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). A set of residues can be used to get a set of integers in an obvious way. Observe...