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Beurling zeta function

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Bateman, Paul T.; Diamond, Harold G. (1969), "Asymptotic distribution of Beurling's generalized prime numbers", in LeVeque, William Judson (ed.),
129: 260: 124:, M.A.A. studies in mathematics, vol. 6, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), pp. 152–210, 42:
A Beurling generalized integer is a number that can be written as a product of Beurling generalized primes. Beurling generalized the usual
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Beurling, Arne (1937), "Analyse de la loi asymptotique de la distribution des nombres premiers généralisés. I",
202: 24: 43: 167: 125: 31:: any sequence of real numbers greater than 1 that tend to infinity. These were introduced by 175: 157: 148: 139: 179: 135: 16:
Riemann zeta function analogue replacing ordinary primes with Beurling generalized primes
206: 249: 32: 82: > 3/2 then the number of Beurling generalized primes less than 171: 194: 162: 46:
to Beurling generalized primes. He showed that if the number
210: 98: = 3/2 then this conclusion need not hold. 27:where the ordinary primes are replaced by a set of 230: 54:) of Beurling generalized integers less than 8: 237: 223: 161: 36: 94:, just as for ordinary primes, but if 7: 191: 189: 14: 156:, Springer Netherlands: 255–291, 193: 108:Abstract analytic number theory 1: 209:. You can help Knowledge by 261:Mathematical analysis stubs 29:Beurling generalized primes 277: 188: 122:Studies in Number Theory 205:–related article is a 23:is an analogue of the 21:Beurling zeta function 203:mathematical analysis 25:Riemann zeta function 256:Zeta and L-functions 44:prime number theorem 163:10.1007/BF02546666 19:In mathematics, a 218: 217: 131:978-0-13-541359-3 86:is asymptotic to 268: 239: 232: 225: 197: 190: 182: 165: 149:Acta Mathematica 142: 276: 275: 271: 270: 269: 267: 266: 265: 246: 245: 244: 243: 186: 145: 132: 119: 116: 104: 70: + O( 58:is of the form 17: 12: 11: 5: 274: 272: 264: 263: 258: 248: 247: 242: 241: 234: 227: 219: 216: 215: 198: 184: 183: 143: 130: 115: 112: 111: 110: 103: 100: 66:) =  15: 13: 10: 9: 6: 4: 3: 2: 273: 262: 259: 257: 254: 253: 251: 240: 235: 233: 228: 226: 221: 220: 214: 212: 208: 204: 199: 196: 192: 187: 181: 177: 173: 169: 164: 159: 155: 152:(in French), 151: 150: 144: 141: 137: 133: 127: 123: 118: 117: 113: 109: 106: 105: 101: 99: 97: 93: 89: 85: 81: 77: 73: 69: 65: 61: 57: 53: 49: 45: 40: 38: 34: 30: 26: 22: 211:expanding it 200: 185: 153: 147: 121: 95: 91: 87: 83: 79: 75: 71: 67: 63: 59: 55: 51: 47: 41: 28: 20: 18: 250:Categories 180:0017.29604 114:References 90:/log  172:0001-5962 74: log 102:See also 33:Beurling 140:0242778 78:) with 35: ( 178:  170:  138:  128:  201:This 207:stub 168:ISSN 126:ISBN 37:1937 176:Zbl 158:doi 39:). 252:: 174:, 166:, 154:68 136:MR 134:, 68:Ax 238:e 231:t 224:v 213:. 160:: 96:γ 92:x 88:x 84:x 80:γ 76:x 72:x 64:x 62:( 60:N 56:x 52:x 50:( 48:N

Index

Riemann zeta function
Beurling
1937
prime number theorem
Abstract analytic number theory
ISBN
978-0-13-541359-3
MR
0242778
Acta Mathematica
doi
10.1007/BF02546666
ISSN
0001-5962
Zbl
0017.29604
Stub icon
mathematical analysis
stub
expanding it
v
t
e
Categories
Zeta and L-functions
Mathematical analysis stubs

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