An elementary proof of the Davenport-Hasse relation
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 extension of some formulae of Lerch
An identity involving Dedekind sums and generalized Kloosterman sums
The various properties of classical Dedekind sums have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of...
An identity involving Ramanujan's sum.
An improvement on Olson's constant for ℤₚ ⊕ ℤₚ
An improvement to Chalk's estimation of exponential sums
An integral transform and its applications.
An upper bound for the number of solutions of a system of congruences
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Appendix on return-time sequences
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...
Arithmetical sums in regular convolutions.
Asymptotic expansions of finite theta series
Automatic sequences generated by synchronizing automata fulfill the Sarnak conjecture
We prove that automatic sequences generated by synchronizing automata satisfy the full Sarnak conjecture. This is of particular interest, since Berlinkov proved recently that almost all automata are synchronizing.
Automorphic forms
Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman I.