311:
154:, with a remark that "the proof is not easy". Hubert Delange found a simpler proof and published it in 1958, together with two other ways of deducing it from results of Erdős and of
141:
208:
Bergelson, Vitaly; Richter, Florian K. (2022), "Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions",
65:
105:
85:
371:
352:
381:
345:
376:
114:
144:
338:
279:
217:
41:
108:
90:
271:
227:
291:
239:
195:
287:
235:
191:
322:
70:
365:
252:
151:
32:
24:
155:
28:
179:
318:
231:
256:
310:
283:
275:
222:
143:
are asymptotically uniformly distributed modulo 1. It implies the
326:
117:
93:
73:
44:
257:"On the distribution function of additive functions"
135:
99:
79:
59:
67:denote the number of prime factors of an integer
150:The theorem was stated without proof in 1946 by
346:
8:
111:. The theorem states that the real numbers
353:
339:
221:
173:
171:
116:
92:
72:
43:
167:
7:
307:
305:
136:{\displaystyle \lambda \omega (n)}
14:
87:, counted with multiplicity, and
309:
180:"On some arithmetical functions"
184:Illinois Journal of Mathematics
27:concerning the distribution of
130:
124:
54:
48:
1:
372:Theorems about prime numbers
325:. You can help Knowledge by
295:; see remark at top of p. 2.
398:
304:
232:10.1215/00127094-2022-0055
60:{\displaystyle \omega (n)}
210:Duke Mathematical Journal
178:Delange, Hubert (1958),
100:{\displaystyle \lambda }
321:-related article is a
137:
101:
81:
61:
16:Distribution of primes
264:Annals of Mathematics
138:
102:
82:
62:
21:Erdős–Delange theorem
145:prime number theorem
115:
91:
71:
42:
35:and Hubert Delange.
31:. It is named after
133:
97:
77:
57:
382:Mathematics stubs
334:
333:
266:, Second Series,
216:(15): 3133–3200,
109:irrational number
80:{\displaystyle n}
389:
355:
348:
341:
313:
306:
296:
294:
261:
249:
243:
242:
225:
205:
199:
198:
175:
142:
140:
139:
134:
106:
104:
103:
98:
86:
84:
83:
78:
66:
64:
63:
58:
23:is a theorem in
397:
396:
392:
391:
390:
388:
387:
386:
362:
361:
360:
359:
302:
300:
299:
276:10.2307/1969031
259:
251:
250:
246:
207:
206:
202:
177:
176:
169:
164:
113:
112:
89:
88:
69:
68:
40:
39:
17:
12:
11:
5:
395:
393:
385:
384:
379:
374:
364:
363:
358:
357:
350:
343:
335:
332:
331:
314:
298:
297:
244:
200:
166:
165:
163:
160:
132:
129:
126:
123:
120:
96:
76:
56:
53:
50:
47:
15:
13:
10:
9:
6:
4:
3:
2:
394:
383:
380:
378:
375:
373:
370:
369:
367:
356:
351:
349:
344:
342:
337:
336:
330:
328:
324:
320:
315:
312:
308:
303:
293:
289:
285:
281:
277:
273:
269:
265:
258:
254:
248:
245:
241:
237:
233:
229:
224:
219:
215:
211:
204:
201:
197:
193:
189:
185:
181:
174:
172:
168:
161:
159:
157:
153:
148:
146:
127:
121:
118:
110:
94:
74:
51:
45:
36:
34:
30:
29:prime numbers
26:
25:number theory
22:
327:expanding it
316:
301:
267:
263:
247:
213:
209:
203:
187:
183:
156:Atle Selberg
149:
37:
20:
18:
319:mathematics
377:Paul Erdős
366:Categories
223:2002.03498
162:References
152:Paul Erdős
33:Paul Erdős
253:Erdős, P.
190:: 81–87,
122:ω
119:λ
95:λ
46:ω
270:: 1–20,
255:(1946),
292:0015424
284:1969031
240:4497225
196:0095809
107:be any
290:
282:
238:
194:
317:This
280:JSTOR
260:(PDF)
218:arXiv
323:stub
38:Let
19:The
272:doi
228:doi
214:171
368::
288:MR
286:,
278:,
268:47
262:,
236:MR
234:,
226:,
212:,
192:MR
186:,
182:,
170:^
158:.
147:.
354:e
347:t
340:v
329:.
274::
230::
220::
188:2
131:)
128:n
125:(
75:n
55:)
52:n
49:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.