Weyl Sums over Integers with Linear Digit Restrictions
نویسندگان
چکیده
Abstract. For any given integer q ≥ 2, we consider sets N of non-negative integers that are defined by linear relations between their q-adic digits (for example, the set of non-negative integers such that the number of 1’s equals twice the number of 0’s in the binary representation). The main goal is to prove that the sequence (αn)n∈N is uniformly distributed modulo 1 for all irrational numbers α. The proof if based on a saddle point analysis of certain generating functions that allows us to bound the corresponding Weyl sums.
منابع مشابه
A 64 Integers 14 ( 2014 ) Tangent Power Sums and Their Applications
For integers m and p, we study the tangent power sums Pm k=1 tan 2p ⇡k 2m+1 . We give recurrence, asymptotic and explicit formulas for these polynomials and indicate their connections with Newman’s digit sums in base 2m. In particular, for increasing m, we prove a monotonic strengthening of the Moser-Newman digit phenomenon for certain intervals.
متن کاملNumbers with fixed sum of digits in linear recurrent number systems
We study the set of integers with a given sum of digits with respect to a linear recurrent digit system. An asymptotic formula for the number of integers ≤ N with given sum of digits is determined, and the distribution in residue classes is investigated, thus generalizing results due to Mauduit and Sárközy. It turns out that numbers with fixed sum of digits are uniformly distributed in residue ...
متن کاملWEYL SUMS IN F q [ x ] WITH DIGITAL RESTRICTIONS MANFRED
Let Fq be a finite field and consider the polynomial ring Fq [X]. Let Q ∈ Fq [X]. A function f : Fq [X] → G, where G is a group, is called strongly Q-additive, if f(AQ + B) = f(A) + f(B) holds for all polynomials A, B ∈ Fq [X] with degB < degQ. We estimate Weyl Sums in Fq [X] restricted by Q-additive functions. In particular, for a certain character E we study sums of the form X
متن کاملOn Weyl’s Inequality, Hua’s Lemma, and Exponential Sums over Binary Forms
1. Introduction. The remarkable success enjoyed by the Hardy-Littlewood method in its application to diagonal diophantine problems rests in large part on the theory of exponential sums in a single variable. Following almost a century of intense investigations , the latter body of knowledge has reached a mature state that, although falling short of what is expected to be true, nonetheless suffic...
متن کاملWeyl sums in Fq[x] with digital restrictions
Let Fq be a finite field and consider the polynomial ring Fq [X]. Let Q ∈ Fq [X]. A function f : Fq [X] → G, where G is a group, is called strongly Q-additive, if f(AQ + B) = f(A) + f(B) holds for all polynomials A,B ∈ Fq [X] with degB < degQ. We estimate Weyl Sums in Fq [X] restricted by Q-additive functions. In particular, for a certain character E we study sums of the form X P E(h(P )), wher...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009