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List of zeta functions

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412: 323:, a function that maps every interval of a poset to the constant value 1. Despite not resembling a holomorphic function, the special case for the poset of integer divisibility is related as a formal Dirichlet series to the Riemann zeta function. 108: 40: 240: 163: 366: 446: 387: 404: 126: 375: 361: 441: 136: 420: 175: 436: 392: 320: 349: 326: 131: 235: 213: 306: 252: 154: 148: 28: 288: 277: 246: 187: 32: 344: 314: 283: 181: 142: 8: 271: 225: 219: 198: 193: 371: 297: 169: 117: 339:
Other functions called zeta functions, but not analogous to the Riemann zeta function
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includes a list of related items that share the same name (or similar names).
381: 121: 17: 204: 103:{\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}.} 411: 274:, like the Riemann zeta function, but only summed over primes 22: 255:, or Mordell–Tornheim zeta function of several variables 43: 102: 428: 417:Index of articles associated with the same name 222:, a generalization of the Riemann zeta function 190:, a generalization of the Riemann zeta function 160:Duursma zeta function of error-correcting codes 409: 405:A directory of all known zeta functions 31:analogous to the original example, the 429: 241:Minakshisundaram–Pleijel zeta function 321:Zeta function of an incidence algebra 367:Birch and Swinnerton-Dyer conjecture 13: 75: 14: 458: 398: 388:Explicit formulae for L-functions 410: 356:Topics related to zeta functions 376:generalized Riemann hypothesis 151:of Beurling generalized primes 120:, related to the zeros of the 53: 47: 1: 327:Zeta function of an operator 127:Arakawa–Kaneko zeta function 7: 333: 210:, a "twisted" zeta function 10: 463: 447:Mathematics-related lists 350:Weierstrass zeta function 329:or spectral zeta function 137:Artin–Mazur zeta function 280:, the archetypal example 176:Hasse–Weil zeta function 132:Arithmetic zeta function 113:Zeta functions include: 236:Matsumoto zeta function 214:Lefschetz zeta function 145:or double zeta function 311:Subgroup zeta function 307:Shintani zeta function 253:Multiple zeta function 155:Dedekind zeta function 149:Beurling zeta function 104: 79: 289:Selberg zeta function 278:Riemann zeta function 247:Motivic zeta function 188:Hurwitz zeta function 164:Epstein zeta function 139:of a dynamical system 105: 59: 33:Riemann zeta function 442:Zeta and L-functions 345:Jacobi zeta function 315:Witten zeta function 284:Ruelle zeta function 228:of a characteristic- 182:Height zeta function 143:Barnes zeta function 41: 272:Prime zeta function 262:-adic zeta function 226:Local zeta function 220:Lerch zeta function 199:Ihara zeta function 194:Igusa zeta function 172:of a function field 166:of a quadratic form 437:Set index articles 372:Riemann hypothesis 170:Goss zeta function 118:Airy zeta function 100: 421:set index article 157:of a number field 95: 454: 414: 362:Artin conjecture 109: 107: 106: 101: 96: 94: 93: 81: 78: 73: 462: 461: 457: 456: 455: 453: 452: 451: 427: 426: 425: 424: 418: 401: 336: 293:Riemann surface 89: 85: 80: 74: 63: 42: 39: 38: 27:is (usually) a 12: 11: 5: 460: 450: 449: 444: 439: 416: 415: 408: 407: 400: 399:External links 397: 396: 395: 390: 385: 379: 369: 364: 358: 357: 353: 352: 347: 341: 340: 335: 332: 331: 330: 324: 318: 317:of a Lie group 312: 309: 304: 295: 286: 281: 275: 269: 256: 250: 244: 243:of a Laplacian 238: 233: 223: 217: 211: 202: 196: 191: 185: 179: 173: 167: 161: 158: 152: 146: 140: 134: 129: 124: 111: 110: 99: 92: 88: 84: 77: 72: 69: 66: 62: 58: 55: 52: 49: 46: 9: 6: 4: 3: 2: 459: 448: 445: 443: 440: 438: 435: 434: 432: 422: 413: 406: 403: 402: 394: 393:Trace formula 391: 389: 386: 383: 382:Selberg class 380: 377: 373: 370: 368: 365: 363: 360: 359: 355: 354: 351: 348: 346: 343: 342: 338: 337: 328: 325: 322: 319: 316: 313: 310: 308: 305: 303: 301: 296: 294: 290: 287: 285: 282: 279: 276: 273: 270: 267: 263: 261: 257: 254: 251: 248: 245: 242: 239: 237: 234: 231: 227: 224: 221: 218: 216:of a morphism 215: 212: 209: 207: 203: 200: 197: 195: 192: 189: 186: 183: 180: 177: 174: 171: 168: 165: 162: 159: 156: 153: 150: 147: 144: 141: 138: 135: 133: 130: 128: 125: 123: 122:Airy function 119: 116: 115: 114: 97: 90: 86: 82: 70: 67: 64: 60: 56: 50: 44: 37: 36: 35: 34: 30: 26: 24: 19: 299: 268:-adic number 265: 259: 229: 205: 184:of a variety 178:of a variety 112: 21: 15: 249:of a motive 18:mathematics 431:Categories 201:of a graph 302:-function 208:-function 76:∞ 61:∑ 45:ζ 374:and the 334:See also 298:Shimizu 29:function 25:function 232:variety 419:This 291:of a 264:of a 23:zeta 20:, a 16:In 433:: 384:S 378:. 300:L 266:p 260:p 230:p 206:L 98:. 91:s 87:n 83:1 71:1 68:= 65:n 57:= 54:) 51:s 48:(

Index

mathematics
zeta
function
Riemann zeta function
Airy zeta function
Airy function
Arakawa–Kaneko zeta function
Arithmetic zeta function
Artin–Mazur zeta function
Barnes zeta function
Beurling zeta function
Dedekind zeta function
Epstein zeta function
Goss zeta function
Hasse–Weil zeta function
Height zeta function
Hurwitz zeta function
Igusa zeta function
Ihara zeta function
L-function
Lefschetz zeta function
Lerch zeta function
Local zeta function
Matsumoto zeta function
Minakshisundaram–Pleijel zeta function
Motivic zeta function
Multiple zeta function
p-adic zeta function
Prime zeta function
Riemann zeta function

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