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Grand Riemann hypothesis

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Conrey and Iwaniec show that sufficiently many small gaps between zeros of the Riemann zeta function would imply the non-existence of Landau–Siegel zeros.
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The Riemann hypothesis: a resource for the aficionado and virtuoso alike
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is the assertion that the nontrivial zeros of all automorphic
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Harmonic Analysis, The Trace Formula, and Shimura Varieties
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You can help Knowledge (XXG) by 540:Riemannian connection on a surface 445:Measurable Riemann mapping theorem 14: 155:-functions should be automorphic. 125:modified grand Riemann hypothesis 69:{\displaystyle {\frac {1}{2}}+it} 713:Unsolved problems in mathematics 635: 613: 612: 525:Riemann's differential equation 435:Hirzebruch–Riemann–Roch theorem 550:Riemann–Hilbert correspondence 420:Generalized Riemann hypothesis 30:generalized Riemann hypothesis 1: 585:Riemann–Siegel theta function 600:Riemann–von Mangoldt formula 698:Mathematical analysis stubs 96:a real number variable and 24:is a generalisation of the 734: 630: 595:Riemann–Stieltjes integral 590:Riemann–Silberstein vector 565:Riemann–Liouville integral 351:Borwein, Peter B. (2008), 222:Clay Mathematics Institute 220:. Vol. 4. Princeton: 151:, asserts that all global 608: 530:Riemann's minimal surface 410: 149:functoriality conjectures 40:lie on the critical line 555:Riemann–Hilbert problems 460:Riemann curvature tensor 425:Grand Riemann hypothesis 415:Cauchy–Riemann equations 22:grand Riemann hypothesis 480:Riemann mapping theorem 647:–related article is a 580:Riemann–Siegel formula 560:Riemann–Lebesgue lemma 495:Riemann series theorem 110: 90: 70: 645:mathematical analysis 520:Riemann zeta function 111: 91: 71: 703:Zeta and L-functions 570:Riemann–Roch theorem 100: 80: 44: 545:Riemannian geometry 455:Riemann Xi function 440:Local zeta function 313:2002AcAri.103..259C 465:Riemann hypothesis 212:; Ellwood, David; 106: 86: 66: 26:Riemann hypothesis 660: 659: 628: 627: 535:Riemannian circle 475:Riemann invariant 366:978-0-387-72125-5 322:10.4064/aa103-3-5 147:, in his general 109:{\displaystyle i} 89:{\displaystyle t} 55: 725: 718:Bernhard Riemann 681: 674: 667: 639: 632: 616: 615: 470:Riemann integral 450:Riemann (crater) 404:Bernhard Riemann 397: 390: 383: 374: 369: 338: 337: 324: 306: 290:Acta Arithmetica 273: 267: 266: 264: 262: 256: 214:Kottwitz, Robert 207: 195: 145:Robert Langlands 115: 113: 112: 107: 95: 93: 92: 87: 75: 73: 72: 67: 56: 48: 733: 732: 728: 727: 726: 724: 723: 722: 688: 687: 686: 685: 629: 624: 604: 515:Riemann surface 490:Riemann problem 406: 401: 367: 357:Springer-Verlag 350: 347: 345:Further reading 342: 341: 281:Iwaniec, Henryk 275: 274: 270: 260: 258: 254: 232: 205: 197: 196: 192: 187: 141: 98: 97: 78: 77: 42: 41: 12: 11: 5: 731: 729: 721: 720: 715: 710: 705: 700: 690: 689: 684: 683: 676: 669: 661: 658: 657: 640: 626: 625: 623: 622: 609: 606: 605: 603: 602: 597: 592: 587: 582: 577: 572: 567: 562: 557: 552: 547: 542: 537: 532: 527: 522: 517: 512: 507: 505:Riemann sphere 502: 500:Riemann solver 497: 492: 487: 482: 477: 472: 467: 462: 457: 452: 447: 442: 437: 432: 427: 422: 417: 411: 408: 407: 402: 400: 399: 392: 385: 377: 371: 370: 365: 346: 343: 340: 339: 297:(3): 259–312. 268: 230: 189: 188: 186: 183: 182: 181: 175: 170:, rather near 156: 140: 137: 118:imaginary unit 105: 85: 65: 62: 59: 54: 51: 13: 10: 9: 6: 4: 3: 2: 730: 719: 716: 714: 711: 709: 706: 704: 701: 699: 696: 695: 693: 682: 677: 675: 670: 668: 663: 662: 656: 654: 650: 646: 641: 638: 634: 621: 620: 611: 610: 607: 601: 598: 596: 593: 591: 588: 586: 583: 581: 578: 576: 573: 571: 568: 566: 563: 561: 558: 556: 553: 551: 548: 546: 543: 541: 538: 536: 533: 531: 528: 526: 523: 521: 518: 516: 513: 511: 508: 506: 503: 501: 498: 496: 493: 491: 488: 486: 483: 481: 478: 476: 473: 471: 468: 466: 463: 461: 458: 456: 453: 451: 448: 446: 443: 441: 438: 436: 433: 431: 428: 426: 423: 421: 418: 416: 413: 412: 409: 405: 398: 393: 391: 386: 384: 379: 378: 375: 368: 362: 358: 354: 349: 348: 344: 336: 332: 328: 323: 318: 314: 310: 305: 300: 296: 292: 291: 286: 282: 278: 277:Conrey, Brian 272: 269: 253: 249: 245: 241: 237: 233: 231:0-8218-3844-X 227: 223: 219: 215: 211: 210:Arthur, James 204: 200: 199:Sarnak, Peter 194: 191: 184: 179: 176: 173: 169: 167: 161: 157: 154: 150: 146: 143: 142: 138: 136: 134: 130: 126: 121: 119: 103: 83: 63: 60: 57: 52: 49: 39: 37: 31: 27: 23: 19: 653:expanding it 642: 617: 485:Riemann form 424: 352: 334: 304:math/0111012 294: 288: 271: 261:November 11, 259:. Retrieved 217: 193: 177: 171: 165: 152: 128: 124: 122: 35: 34:automorphic 21: 15: 708:Conjectures 510:Riemann sum 160:Siegel zero 18:mathematics 692:Categories 185:References 164:Dirichlet 38:-functions 331:0065-1036 248:637721920 240:1534-6455 133:real line 619:Category 283:(2002). 252:Archived 216:(eds.). 201:(2005). 309:Bibcode 168:-series 363:  329:  246:  238:  228:  20:, the 643:This 299:arXiv 255:(PDF) 208:. In 206:(PDF) 139:Notes 76:with 649:stub 361:ISBN 327:ISSN 263:2020 244:OCLC 236:ISSN 226:ISBN 174:= 1. 158:The 123:The 116:the 28:and 317:doi 295:103 16:In 694:: 359:, 333:. 325:. 315:. 307:. 293:. 287:. 279:; 250:. 242:. 234:. 135:. 120:. 680:e 673:t 666:v 655:. 396:e 389:t 382:v 319:: 311:: 301:: 265:. 178:L 172:s 166:L 153:L 129:L 104:i 84:t 64:t 61:i 58:+ 53:2 50:1 36:L

Index

mathematics
Riemann hypothesis
generalized Riemann hypothesis
automorphic L-functions
imaginary unit
real line
Robert Langlands
functoriality conjectures
Siegel zero
Dirichlet L-series
Sarnak, Peter
"Notes on the Generalized Ramanujan Conjectures"
Arthur, James
Kottwitz, Robert
Clay Mathematics Institute
ISBN
0-8218-3844-X
ISSN
1534-6455
OCLC
637721920
Archived
Conrey, Brian
Iwaniec, Henryk
"Spacing of zeros of Hecke L-functions and the class number problem"
Acta Arithmetica
arXiv
math/0111012
Bibcode
2002AcAri.103..259C

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