Dirichlet Series Associated with Strongly q-Multiplicative Functions

详细信息    查看全文

• 作者：Giedrius Alkauskas
• 关键词：Dirichlet series ; strongly q ; multiplicative functions
• 刊名：The Ramanujan Journal
• 出版年：2004
• 出版时间：March 2004
• 年：2004
• 卷：8
• 期：1
• 页码：13-21
• 全文大小：96 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Number Theory
  Field Theory and Polynomials
  Combinatorics
  Fourier Analysis
  Functions of a Complex Variable
  
• 出版者：Springer U.S.
• ISSN：1572-9303

文摘

In this work the Dirichlet series k\textf(s\text) = ?_n￥ \fracf(n - 1)ns \kappa {\text{f(}}s{\text{) = }}\sum\nolimits_n^\infty {\frac{{f(n - 1)}}{{n^s }}} associated with real strongly q-multiplicative functions f(n) are studied. We will confine ourselves to the case d_f L _f (\fractq) = ò₀t L _f (u) du \delta _f \Lambda _f (\frac{t}{q}) = \int_0^t {\Lambda _f (u) du} for some nonzero real ?s \leqslant - k₀ ,|ás| \leqslant \fracp2lnq\Re s \leqslant - k_0 ,|\Im s| \leqslant \frac{\pi }{{2\ln q}} the function _f(s) has only trivial zeros which are simple.