Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

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(6.99725,2.00426) (7.02650,2.03103) (7.05575,2.05779) (7.08500,2.08454) (7.11425,2.11125) (7.14350,2.13793) (7.17275,2.16455) (7.20200,2.19110) (7.23125,2.21758) (7.26050,2.24396) (7.28975,2.27024) (7.31900,2.29640) (7.34825,2.32243) (7.37750,2.34833) (7.40675,2.37406) (7.43600,2.39964) (7.46525,2.42504) (7.49450,2.45024) (7.52375,2.47525) (7.55300,2.50005) (7.58225,2.52462) (7.61150,2.54895) (7.64075,2.57304) (7.67000,2.59687) (7.69925,2.62043) (7.72850,2.64371) (7.75775,2.66670) (7.78700,2.68938) (7.81625,2.71175) (7.84550,2.73380) (7.87475,2.75552) (7.90400,2.77689) (7.93325,2.79791) (7.96250,2.81856) (7.99175,2.83884) (8.02100,2.85874) (8.05025,2.87824) (8.07950,2.89735) (8.10875,2.91604) (8.13800,2.93431) (8.16725,2.95216) (8.19650,2.96957) (8.22575,2.98654) (8.25500,3.00305) (8.28425,3.01911) (8.31350,3.03469) (8.34275,3.04980) (8.37200,3.06443) (8.40125,3.07857) (8.43050,3.09222) (8.45975,3.10536) (8.48900,3.11800) (8.51825,3.13012) (8.54750,3.14173) (8.57675,3.15280) (8.60600,3.16335) (8.63525,3.17336) (8.66450,3.18284) (8.69375,3.19177) (8.72300,3.20015) (8.75225,3.20797) (8.78150,3.21525) (8.81075,3.22196) (8.84000,3.22811) (8.86925,3.23369) (8.89850,3.23871) (8.92775,3.24316) (8.95700,3.24703) (8.98625,3.25033) (9.01550,3.25305) (9.04475,3.25520) (9.07400,3.25677) (9.10325,3.25776) (9.13250,3.25817) (9.16175,3.25800) (9.19100,3.25725) (9.22025,3.25592) (9.24950,3.25402) (9.27875,3.25153) (9.30800,3.24847) (9.33725,3.24484) (9.36650,3.24063) (9.39575,3.23585) (9.42500,3.23050) (9.45425,3.22459) (9.48350,3.21811) (9.51275,3.21107) (9.54200,3.20347) (9.57125,3.19532) (9.60050,3.18662) (9.62975,3.17737) (9.65900,3.16758) (9.68825,3.15725) (9.71750,3.14640) (9.74675,3.13501) (9.77600,3.12310) (9.80525,3.11068) (9.83450,3.09775) (9.86375,3.08431) (9.89300,3.07037) (9.92225,3.05595) (9.95150,3.04103) (9.98075,3.02564) (10.01000,3.00978) (10.03925,2.99346) (10.06850,2.97668) (10.09775,2.95945) (10.12700,2.94179) (10.15625,2.92369) (10.18550,2.90517) (10.21475,2.88624) (10.24400,2.86690) (10.27325,2.84716) (10.30250,2.82704) (10.33175,2.80654) (10.36100,2.78567) (10.39025,2.76445) (10.41950,2.74287) (10.44875,2.72096) (10.47800,2.69872) (10.50725,2.67616) (10.53650,2.65330) (10.56575,2.63014) (10.59500,2.60670) (10.62425,2.58298) (10.65350,2.55900) (10.68275,2.53476) (10.71200,2.51029) (10.74125,2.48559) (10.77050,2.46067) (10.79975,2.43554) (10.82900,2.41022) (10.85825,2.38472) (10.88750,2.35905) (10.91675,2.33322) (10.94600,2.30724) (10.97525,2.28113) (11.00450,2.25490) (11.03375,2.22856) (11.06300,2.20212) (11.09225,2.17560) (11.12150,2.14901) (11.15075,2.12235) (11.18000,2.09565) (11.20925,2.06892) (11.23850,2.04216) (11.26775,2.01539) (11.29700,1.98863) (11.32625,1.96188) (11.35550,1.93516) (11.38475,1.90848) (11.41400,1.88185) (11.44325,1.85529) (11.47250,1.82881) (11.50175,1.80241) (11.53100,1.77612) (11.56025,1.74995) (11.58950,1.72390) (11.61875,1.69800) (11.64800,1.67224) (11.67725,1.64665) (11.70650,1.62123) (11.73575,1.59600) (11.76500,1.57097) (11.79425,1.54616) (11.82350,1.52156) (11.85275,1.49720) (11.88200,1.47309) (11.91125,1.44923) (11.94050,1.42564) (11.96975,1.40234) (11.99900,1.37932) (12.02825,1.35660) (12.05750,1.33419) (12.08675,1.31211) (12.11600,1.29036) (12.14525,1.26895) (12.17450,1.24790) (12.20375,1.22721) (12.23300,1.20689) (12.26225,1.18695) (12.29150,1.16740) (12.32075,1.14826) (12.35000,1.12952)};
24 \draw[fill=white] (2.77215,2.02182) circle (0.07);
25 \draw[fill=white] (7.01644,2.02182) circle (0.07);
26 \draw[fill=white] (11.26073,2.02182) circle (0.07);
27 \node[] at (6.50000,4.70000) {$\frac32e^{-t/2}D_3(t)=\cos(\sqrt3t/2)+\frac12e^{-3t/2}$};
28 \node[] at (6.50000,-0.25000) {solid: full expression; dashed: two-term model; circles: model zeros};
29 \end{tikzpicture}

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Back to Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data