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Λ3(sk)和它的延拓

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 楼主| 发表于 2023-12-23 11:08 | 显示全部楼层
4*11^2区域的实际绝对下界偶数:
D(128)=3
D(152)=4
D(188)=5
D(332)=6
D(398)=7
D(2n)=8
D(2n)=9
D(2n)=10
D(2n)=11
D(2n)=12
的计算下界
1156/484=2.3884297520661157024793388429752
5.3884297520661157024793388429752
128*5.3884297520661157024793388429752=689.71900826446280=688,D(688)>9
152*5.3884297520661157024793388429752=819.04132231404958=818,D(818)>10
188*5.3884297520661157024793388429752=1013.0247933884=1013,D(1013)>11
332*5.3884297520661157024793388429752=1788.9586776859=1788,D(1788)>12
398*5.3884297520661157024793388429752=2144.5950413223=2144,D(2144)>13
D(2n)=8
D(2n)=9
D(2n)=10
D(2n)=11
D(2n)=12
的实际绝对下界偶数
D(488)=9
D(632)=10
D(692)=11
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 楼主| 发表于 2023-12-24 09:22 | 显示全部楼层
4*17^2区域的实际绝对下界偶数:
D(488)=9
D(632)=10
D(692)=11
D(992)=13
D(1112)=16
D(1412)=18
D(1448)=20
D(1718)=21
D(2048)=25
D(2252)=26
D(2672)=28
D(2936)=31
D(2978)=34
D(3092)=35
D(3218)=37
D(3272)=38
D(3296)=39
D(2n)=40
D(2n)=41
D(2n)=42
D(2n)=43
D(2n)=44
D(2n)=45
D(2n)=46
D(2n)=47
D(2n)=48
D(2n)=49
D(2n)=50
D(2n)=51
D(2n)=52
D(2n)=53
D(2n)=54
D(2n)=56
D(2n)=57
计算下界偶数:
3364/1156=2.9100346020761245674740484429066
5.9100346020761245674740484429066
488*5.9100346020761245674740484429066=2884.09688581314=2884,D(2884)>26
632*5.9100346020761245674740484429066=3735.14186851211=3734,D(3734)>41
692*5.9100346020761245674740484429066=4089.74394463667=4088,D(4089)>43
992*5.9100346020761245674740484429066=5862.75432525951=5862,D(5862)>44
1112*5.9100346020761245674740484429066=6571.958477508=6570,D(6570)>45
1412*5.9100346020761245674740484429066=8344.968858131=8344,D(8344)>46
1448*5.9100346020761245674740484429066=8557.730103806=8556,D(8556)>48
1718*5.9100346020761245674740484429066=10153.4394463=10152,D(10152)>50
2048*5.9100346020761245674740484429066=12103.7508650=12102,D(12102)>51
2252*5.9100346020761245674740484429066=13309.3979238=13308,D(13308)>52
2672*5.9100346020761245674740484429066=15791.6124567=15790,D(15790)>54
2936*5.9100346020761245674740484429066=17351.8615916=17350,D(17350)>55
2978*5.9100346020761245674740484429066=17600.0830449=17600,D(17600)>59
3092*5.9100346020761245674740484429066=18273.8269896=18272,D(18272)>60
3218*5.9100346020761245674740484429066=19018.4913494=19018,D(19018)>61
3272*5.9100346020761245674740484429066=19337.6332179=19336,D(19336)>64
3296*5.9100346020761245674740484429066=19479.4740484=19478,D(19479)>66
D(2n)=40
D(2n)=41
D(2n)=42
D(2n)=43
D(2n)=44
D(2n)=45
D(2n)=46
D(2n)=47
D(2n)=48
D(2n)=49
D(2n)=50
D(2n)=51
D(2n)=52
D(2n)=53
D(2n)=54
D(2n)=56
D(2n)=57
的实际绝对下界偶数
D(3632)=40
D(3754)=42
D(4022)=43
D(4058)=44
D(4412)=45
D(4448)=46
D(4478)=48
D(4688)=50
D(5078)=51
D(5468)=52
D(5528)=54
D(5948)=55
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 楼主| 发表于 2023-12-26 09:31 | 显示全部楼层
绝对下界系数c

我们用c2n/ln^2(2n)来表示绝对下界函数.
我们有

D(12)=1,c=0.51456342151338530185239000804185
D(68)=2,c=0.52365427276589806389426802470844
D(128)=3,c=0.55177025817168444864112555757829
D(152)=4,c=0.66419409178259614009879467493721
D(188)=5,c=0.72926394760868008346632926613335
D(332)=6,c=0.60902877121693446495740007100965
D(398)=7,c=0.63030968161059913952920765310612
D(488)=9,c=0.70672140044156829560895707299192
D(632)=10,c=0.65804073446107312949098843361338
D(692)=11,c=0.67980929072258750441617563445777
D(992)=13,c=0.62387129681815591032627529150801
D(1112)=16,c=0.70784187464441136729049996382815
D(1412)=18,c=0.66851451991068414361255904294107
D(1448)=20,c=0.73160759491119246336056580476003
D(1718)=21,c=0.67823828472502210794803047102007
D(2048)=25,c=0.70965349956179653789940680768463
D(2252)=26,c=0.6880050563796536952647710612843
D(2672)=28,c=0.6524386963377056693446757256216
D(2936)=31,c=0.67318448240944685627145875961156
D(2978)=34,c=0.73051039540496292727854686232008
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 楼主| 发表于 2023-12-31 09:44 | 显示全部楼层
D(345502)=1590,c=0.74843571459697982335431255912874
D(346328)=1614,c=0.75820473583596260206814741054566
D(352448)=1624,c=0.75171560710128253443791033486441
D(354152)=1640,c=0.75603981909008297512742441370824
D(357584)=1647,c=0.75311514549034225275006599543945
D(358712)=1669,c=0.7611499158272099985070231605856
D(358744)=1677,c=0.76474077461529210847570143028723
D(359378)=1678,c=0.76405777637870198255579869218863
D(360758)=1680,c=0.7624989304166443926635193946154
D(360896)=1683,c=0.76361409424095340394315662741575


我们从偶数12一直计算到偶数360896,c都大于0.51456342151338530185239000804185为了计算方便我们取c为0.5
另一方面我们从D(2n)的单纪法D(2n)的双筛法考虑D(2n)一定大于2n/ln^2(2n),换成双纪法就是0.5(2n)/ln^2(2n).

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 楼主| 发表于 2024-1-5 09:29 | 显示全部楼层
利用D(2n)>0.5(2n)/ln^2(2n)
我们得到
实际值D(345502)=1590
计算值D(345502)=1062.215477555202278662077030114=1062
我们不求正确值就可得到2n>345502,D(2n)>1062

实际值D(346328)=1614
计算值D(346328)>1064.3563167806356734192518757455=1064
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 楼主| 发表于 2024-1-8 09:05 | 显示全部楼层
实际值D(352448)=1624
计算值D(352448)>1080.1957446795368148978854621135=1080

实际值D(354152)=1640
计算值D(354152)>1084.5989580110939884798001415584=1084
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 楼主| 发表于 2024-1-10 09:51 | 显示全部楼层
实际值D(357584)=1647
计算值D(357584)>1093.4582911140781775765317213307=1092

实际值D(358712)=1669
计算值D(358712)>1096.3674601383537892608233260589=1096
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 楼主| 发表于 2024-1-13 15:56 | 显示全部楼层
实际值D(358744)=1677
计算值D(358744)>1096.4499708045683276533858233875=1096

实际值D(359378)=1678
计算值D(359378)>1098.0844982384594218216633663264=1098
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 楼主| 发表于 2024-1-16 15:50 | 显示全部楼层
实际值D(360758)=1680
计算值D(360758)>1101.6408895695204459264066323932=1100

实际值D(360896)=1683
计算值D(360896)>1101.9964224684284191237718081074=1100
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 楼主| 发表于 2024-1-17 10:06 | 显示全部楼层
计算值D(1000000)>2619.6069029390823502772337495148=2618
计算值D(10000000)>19246.091531797339716322533669904=19246
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