How to recover anL-series from its values at almost all positive integers. Some remarks on a formula of Ramanujan
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We define a class of analytic functions which can be obtained from their values at almost all positive integers by a canonical interpolation procedure. All the usualL-functions belong to this class which is interesting in view of the extensive investigations of special values of motivicL-series. A number of classical contour integral formulas appear as particular cases of the interpolation scheme. The paper is based on a formula of Ramanujan and results of Hardy. An approach to the problem via distributions is also presented.
KeywordsInterpolation formulas analytic functions contour integrals special values L-functions
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