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Erdős–Delange theorem

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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",
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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:(

Index

number theory
prime numbers
Paul Erdős
irrational number
prime number theorem
Paul Erdős
Atle Selberg


"On some arithmetical functions"
MR
0095809
arXiv
2002.03498
doi
10.1215/00127094-2022-0055
MR
4497225
Erdős, P.
"On the distribution function of additive functions"
doi
10.2307/1969031
JSTOR
1969031
MR
0015424
Stub icon
mathematics
stub
expanding it

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