Approximate Functional Equation for the Product of Functions and Divisor Problem

Details Approximate Functional Equation for the Product of Functions and Divisor Problem Approximate Functional Equation for the Product of Functions and Divisor Problem

2005-02-07

arxiv.org/abs/math/0502126v2

Mathematics

Number Theory

24 pages

Scientific paper

For functions defined via Dirichlet/generalized Dirichlet series in some half planes of the complex plane, we give a new simple elementary approach to obtain an Approximate Functional Equation(AFE for short) for the product of functions with explicit remainder term. We do this,using a highly generalized identity following Motohashi's approach,wherein he uses a generalisation of Dirichlet's device.We use our method to give an AFE for the product of two Dirichlet L-series corresponding to primitive Dirichlet characters with hitherto unknown estimate for its remainder term.We also consideer AFEs of functions on the real line and the AFEs not only of the r-th power of Dirichlet L-series(or,of Riemann Zeta function)but also of the r-th root of it,where r is a positive integer

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