/*** EXAMPLE: Eisenstein series G_k, k>2 even ***/ /*** v1.2, July 2013, questions to tim.dokchitser@bristol.ac.uk ***/ /*** ***/ /*** type \rex-eisen or read("ex-eisen") at gp prompt to run this ***/ read("computel"); \\ read the ComputeL package \\ and set the default values default(realprecision,40); \\ set working precision; used throughout K = 16; \\ Our modular form is G_K with this K \\ may change this to any even K conductor = 1; \\ exponential factor gammaV = [0,1]; \\ list of gamma-factors weight = K; \\ L(s)=sgn*L(weight-s) sgn = (-1)^(K/2); \\ sign in the functional equation \\ It has a simple pole in s=K Lpoles = [K]; Lresidues = [(-1)^(K/2)*sqrt(Pi)*bernfrac(K)/K]; initLdata("sigma(k,K-1)"); \\ initialize L-series \\ Coefficients given by the divisor function print("EXAMPLE: L-function associated to the modular form G_",K," of weight ",K); print(" coefficients = divisor function sigma(n,",K-1,")"); print(" with ",default(realprecision)," digits precision"); print("Verifying functional equation. Error: ",errprint(checkfeq())); print("L(1) = ",lval = L(1)); print(" (check) = ",lval2 = L(1,1.1)," (err=",errprint(lval-lval2),")");