Short character sums with Beatty sequences
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This article is published in Mathematical Research Letters.The article was published on 2006-01-01 and is currently open access. It has received 30 citations till now. The article focuses on the topics: Character (mathematics).read more
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Prime numbers with beatty sequences
TL;DR: In this article, the authors give an asymptotic formula for the number of primes p = qbn + c + a with n N, where n N is a real number such that is positive and irrational of nite type (which is true for almost all ).
Journal ArticleDOI
Density of non-residues in Burgess-type intervals and applications
TL;DR: In this article, it was shown that for any fixed e> 0, there are numbers δ> 0 and p0 2 with the following property: for every prime p p0 and every integer N such that p 1/(4 √ e )+e N p, the sequence 1, 2,...,N contains at least δN quadratic non-residues modulo p.
Journal ArticleDOI
Non-residues and primitive roots in beatty sequences
TL;DR: In this paper, the authors studied multiplicative character sums taken on the values of a nonhomogeneous Beatty sequence where α,β ∈ ℝ, and α is irrational.
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Arithmetic functions on Beatty sequences
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Open problems on exponential and character sums
TL;DR: In this paper, a collection of mostly unrelated open questions, at various levels of difficulty, related to exponential and multiplicative character sums is presented, which can be used by the beginners in this area as an entry point to gain some immediate hands-on experience with exponential and character sums.
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Book
An Introduction to the Theory of Numbers
TL;DR: The fifth edition of the introduction to the theory of numbers has been published by as discussed by the authors, and the main changes are in the notes at the end of each chapter, where the author seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present a reasonably accurate account of the present state of knowledge.
Book
Analytic Number Theory
Henryk Iwaniec,Emmanuel Kowalski +1 more
TL;DR: In this paper, the critical zeros of the Riemann zeta function are defined and the spacing of zeros is defined. But they are not considered in this paper.