论文标题
加性表示功能和离散卷积
Additive representation functions and discrete convolutions
论文作者
论文摘要
对于$ a $ a $的非阴性整数，令$ r_a（n）$表示方程的解决方案$ n = a+a'$ a $ a $ a $，$ a'\ in a $ in a $。用$χ_a（n）$表示$ a $的特征函数。令$ b_n> 0 $为满足$ \ limsup_ {n \ to \ infty} b_n <1 $的序列。在本文中，我们证明了一些以$ r_a（n）= \ sum_ = \ sum_ {k = 0}^nχ_a（k）χ_a（k）χ_a（n-k）$和$ sum_和$ \ sum_ = 0} n = 0}^nr_a（n} nr_a（n} nr_a（n} nr_a（n）， $ \ sum_ {k = 0}^nb_kb_ {n-k} $和$ \ sum_ {n = 0}^n \ sum_ {k = 0}^nb_kb_ {n-kb_ {n-k} $。
For a set $A$ of non-negative integers, let $R_A(n)$ denote the number of solutions to the equation $n=a+a'$ with $a$, $a'\in A$. Denote by $χ_A(n)$ the characteristic function of $A$. Let $b_n>0$ be a sequence satisfying $\limsup_{n\to \infty}b_n<1$. In this paper, we prove some Erd\H os--Fuchs-type theorems about the error terms appearing in approximation formulæ for $R_A(n)=\sum_{k=0}^nχ_A(k)χ_A(n-k)$ and $\sum_{n=0}^NR_A(n)$ having principal terms $\sum_{k=0}^nb_kb_{n-k}$ and $\sum_{n=0}^N\sum_{k=0}^nb_kb_{n-k}$, respectively.
