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Chebotarev theorem on roots of unity

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Candes, Emmanuel J; Romberg Justin K; Tao, Terence (2006). "Stable signal recovery from incomplete and inaccurate measurements".
533: 102: 31: 300: 383: 378: 255: 82: 67:". Several proofs have been proposed since, and it has even been discovered independently by 496: 468:
Collection of Articles Dedicated to Alberto González Domınguez on His Sixty-fifth Birthday
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Stevenhagen, Peter; Lenstra, Hendrik W (1996). "Chebotarev and his density theorem".
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All submatrices of a discrete Fourier transform matrix of prime length are invertible
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Frenkel, PE (2003). "Simple proof of Chebotarev's theorem on roots of unity".
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was the first to prove it, in the 1930s. This proof involves tools from
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Dieudonné, Jean (1970). "Une propriété des racines de l'unité".
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does meet the requirements of mathematical esthetics
162:{\displaystyle a_{ij}=\omega ^{ij},1\leq i,j\leq n} 264: 244: 224: 161: 91: 525: 465: 479:Communications on Pure and Applied Mathematics 424: 407: 490: 441: 413: 382: 218: 14: 526: 63:, who made comments arguing that it " 18:Chebotaryov theorem on roots of unity 41:was originally a conjecture made by 39:Chebotarev theorem on roots of unity 539:Theorems in algebraic number theory 24: 259: 191: 86: 25: 550: 283:of prime length are invertible. 286: 371:The Mathematical Intelligencer 349: 340: 331: 322: 313: 13: 1: 430:Mathematical Research Letters 362: 74: 32:Chebotarev's density theorem 7: 452:10.4310/MRL.2005.v12.n1.a11 252:is prime then any minor of 10: 555: 534:Theorems in linear algebra 346:Candès, Romberg, Tao, 2006 295:, the theorem was used by 29: 99:be a matrix with entries 319:Stevenhagen et al., 1996 306: 30:Not to be confused with 265:{\displaystyle \Omega } 92:{\displaystyle \Omega } 266: 246: 226: 163: 93: 301:uncertainty principle 267: 247: 227: 164: 94: 256: 236: 173: 103: 83: 501:2005math......3066C 393:10.1007/BF03027290 337:J. DieudonnĂ©, 1970 328:P.E. Frenkel, 2003 275:Equivalently, all 262: 242: 222: 159: 89: 45:in the context of 509:10.1002/cpa.20124 293:signal processing 245:{\displaystyle n} 16:(Redirected from 546: 520: 494: 485:(8): 1207–1223. 471: 462: 445: 419: 417: 404: 386: 356: 353: 347: 344: 338: 335: 329: 326: 320: 317: 271: 269: 268: 263: 251: 249: 248: 243: 231: 229: 228: 223: 221: 207: 206: 202: 194: 168: 166: 165: 160: 134: 133: 118: 117: 98: 96: 95: 90: 21: 554: 553: 549: 548: 547: 545: 544: 543: 524: 523: 384:10.1.1.116.9409 365: 360: 359: 354: 350: 345: 341: 336: 332: 327: 323: 318: 314: 309: 289: 257: 254: 253: 237: 234: 233: 217: 198: 190: 186: 182: 174: 171: 170: 126: 122: 110: 106: 104: 101: 100: 84: 81: 80: 77: 47:lacunary series 35: 28: 23: 22: 15: 12: 11: 5: 552: 542: 541: 536: 522: 521: 473: 472: 463: 436:(1): 121–127, 421: 420: 405: 364: 361: 358: 357: 348: 339: 330: 321: 311: 310: 308: 305: 299:to extend the 288: 285: 261: 241: 220: 216: 213: 210: 205: 201: 197: 193: 189: 185: 181: 178: 158: 155: 152: 149: 146: 143: 140: 137: 132: 129: 125: 121: 116: 113: 109: 88: 76: 73: 26: 9: 6: 4: 3: 2: 551: 540: 537: 535: 532: 531: 529: 518: 514: 510: 506: 502: 498: 493: 488: 484: 480: 475: 474: 469: 464: 461: 457: 453: 449: 444: 439: 435: 431: 427: 423: 422: 416: 411: 406: 402: 398: 394: 390: 385: 380: 376: 372: 367: 366: 352: 343: 334: 325: 316: 312: 304: 302: 298: 294: 284: 282: 278: 273: 272:is non-zero. 239: 214: 211: 208: 203: 199: 195: 187: 183: 179: 176: 156: 153: 150: 147: 144: 141: 138: 135: 130: 127: 123: 119: 114: 111: 107: 72: 70: 66: 62: 58: 57:Galois theory 54: 50: 48: 44: 40: 33: 19: 492:math/0503066 482: 478: 467: 443:math/0308286 433: 429: 415:math/0312398 377:(2): 26–37. 374: 370: 355:T. Tao, 2003 351: 342: 333: 324: 315: 290: 287:Applications 274: 78: 64: 59:and pleased 51: 38: 36: 426:Terence Tao 277:submatrices 528:Categories 363:References 281:DFT matrix 53:Chebotarev 517:119159284 379:CiteSeerX 260:Ω 215:∈ 196:π 177:ω 154:≤ 142:≤ 124:ω 87:Ω 75:Statement 69:DieudonnĂ© 61:Ostrowski 43:Ostrowski 401:14089091 169:, where 497:Bibcode 460:8548232 515:  458:  399:  381:  297:T. Tao 232:. If 513:S2CID 487:arXiv 456:S2CID 438:arXiv 410:arXiv 397:S2CID 307:Notes 279:of a 79:Let 37:The 505:doi 448:doi 389:doi 291:In 530:: 511:. 503:. 495:. 483:59 481:. 454:, 446:, 434:12 432:, 395:. 387:. 375:18 373:. 303:. 71:. 49:. 519:. 507:: 499:: 489:: 470:. 450:: 440:: 418:. 412:: 403:. 391:: 240:n 219:N 212:n 209:, 204:n 200:/ 192:i 188:2 184:e 180:= 157:n 151:j 148:, 145:i 139:1 136:, 131:j 128:i 120:= 115:j 112:i 108:a 34:. 20:)

Index

Chebotaryov theorem on roots of unity
Chebotarev's density theorem
Ostrowski
lacunary series
Chebotarev
Galois theory
Ostrowski
Dieudonné
submatrices
DFT matrix
signal processing
T. Tao
uncertainty principle
CiteSeerX
10.1.1.116.9409
doi
10.1007/BF03027290
S2CID
14089091
arXiv
math/0312398
Terence Tao
arXiv
math/0308286
doi
10.4310/MRL.2005.v12.n1.a11
S2CID
8548232
arXiv
math/0503066

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