| Abstrakt: |
Abstract We prove the following statement. Let $$ q \ge 2 $$, $$ q \in \mathbb{N} $$ and let $$ t:\mathbb{N}_0 \to \mathbb{R} $$. Suppose that, for all $$ v \in \mathbb{N} $$ and $$ 0 \le a_1, a_2 $$ \eta_{{a_1, a_2 }} \left( b \right): = t\left( {a_1 + bq^v } \right) - t\left( {a_2 + bq^v } \right) $$ satisfies the relation $$ \frac{1}{x}\sum\limits_{b where e(u) : = e2πiu . Then $$ \mathop {\sup }\limits_{{g \in \tilde{\mathcal{M}}_q }} \left| {\frac{1}{x}\sum\limits_{n where $$ \tilde{\mathcal{M}}_q $$ q is the set of q-multiplicative functions g such that $$ \left| {g\left( n \right)} \right| \le 1\left( {n = 1,2,...} \right) $$. [ABSTRACT FROM AUTHOR] |
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