User christian.selinger - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T07:14:39Z http://mathoverflow.net/feeds/user/6480 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/26738/analytical-continuation-of-a-dirichlet-series-with-periodic-coefficients Analytical continuation of a Dirichlet series with periodic coefficients christian.selinger 2010-06-01T16:54:32Z 2010-06-01T20:11:34Z <p>Fix a complex number s and a real number x, does there exist an analytic continuation of the Dirichlet series </p> <p>$L(s,x):=\sum_{k=1}^{\infty}\frac{\sin^2(2\pi k x)}{k^s}$</p> <p>to the whole complex plane except 1?</p> <p>If yes, is there some functional equation verified which makes it possible to calculate $L(0,x)$?</p> <p>If yes, what about the modulus of continuity of $x\mapsto L(0,x)$? ($L(\frac{3}{2},x)$ seems to be a nice case.)</p> <p>Thanks for any comments Chri</p>