A shortened equation for convolutions
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Abstract
The zeta functions of convolutions are Dirichlet series of the general form\(\sum\limits_{n = 1}^\infty {a_n n^{ - 3} } \) therefore, they are well convergent in the right half-plane Res>1. In the critical strip Res ∈(0,1) the convolutions can be represented in terms of the Linnik-selberg zeta functions whose coefficients are Kloosterman sums. In the present paper, these two representations are combined into a single representation in the same way as the shortened equation for the classical Riemann zeta function. Bibliography: 10 titles.
Keywords
Convolution Functional Equation Zeta Function Dirichlet Series Riemann Zeta Function
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© Plenum Publishing Corporation 1997