2900 



Distribution of Prime Numbers 



2900 



Function (N) , asymptotic expression. Mertens, 



F. Crelle J. Mth. 77 (1874) 289-. 



</< (m). Poreckij, P. S. Kazan S. Nt. (Ps.- 

 Mth.) P. 6 (1888) 52-; Fschr. Mth. (1888) 171. 



-F(-) = l or as y is < x, formula con- 



cerning. Cavallin, C. B. S. N. Ts. Mth. 



5 (B) (1894) 33-; Fschr. Mth. (1893-94) 266-. 

 Functions giving real prime numbers. Gegen- 

 bauer, L. Mh. Mth. Ps. 7 (1896) 73-. 



in theory of numbers. Daublebsky von 

 Sterneck, E. Mh. Mth. Ps. 7 (1896) 37-. 



, calculation of certain. 

 Daublebsky von Sterneck, E. Mh. Mth. Ps. 

 9 (1898) 43-. 



'A (Pi <?) an d X (P> <?)> series connected with. 

 Lerch, M. Prag Sb. (1894) (Mth.-Nt.) No. 

 33, 16 pp. 



Infinitesimal analysis, applications. Lejeune- 



Dirichlet, G. Crelle J. 19 (1839) 324- ; 21 



(1840) 1-, 134-. 

 Integral calculus, applications. Lucas, E. 



C. E. 82 (1876) 1303-. 



, . Weber, H. Gott. Nr. (1896) 275-. 



Lambert's series. Scherk, H. F. Crelle J. 9 



(1832) 162-. 



. Schldfii,L. Grunert Arch. 10 (1847) 332-. 



. Cesdro, E. G. Teix. J. Sc. 6 (1885) 91-. 



in asymptotic arithmetic. Cesdro, E. 

 Nap. Ed. 32 (1893) 197-. 



as definite integral. Schlomilch, 0. 

 Schlomilch Z. 6 (1861) 407-. 



generalised. Cesdro, E. 



6 (1885) 19-. 



and law of primes. Curtze, M. [1867] 



A. Mt. 1 (1867-68) 285-. 



, transformations. Cesdro, E. N. A. 

 Mth. 7 (1888) 374-. 



Law of prime numbers. Burhenne, H. Grunert 



Arch. 19 (1852) 442-. 

 Lemniscate functions and complex integers, 



theorem of reciprocity. Bonaventura, P. 



G. Mt. 30 (1892) 300-. 



Linear forms, theorem on sum of pkh powers. 



Minkowski, H. C. E. 112 (1891) 209-. 

 Logarithms of large numbers. Le Barbier, . 



Gergonne A. Mth. 20 (1829-30) 366-. 

 Numerical products in which exponents depend 



on numbers. Glaisher, J. W. L. Mess. 



Mth. 23 (1894) 145- ; 25 (1896) 186. 

 Series connected with prime numbers. Eogel, 



F. Prag Sb. (1895) (Mth.-Nt.) No. 22, 11 pp. 



in theory of number s , transformation . Eogel , 

 F. Prag Sb. (1897) (Mth.-Nt.) No. 51, 31 pp. 



, trigonometric, functions in theory of 



numbers represented by. Eogel, F. Arch. 



Mth. Ps. 10 (1891) 62-. 

 Sums of powers of divisors, relations between. 



Eogel, F. Prag Sb. (1897) (Mth.-Nt.) No. 1, 



9pp. 



Polignac, A. (Prince de). Liouv. J. Mth. 19 

 (1854) 305- ; C. E. 45 (1857) 406-, 431-, 

 575-, 882-; 49 (1859) 350-, 386-, 624-, 724-. 



Lebesgue, V.A. N. A. Mth. 15 (1856) 130-, 236-. 



Mertens, F. Crelle J. Mth. 78 (1874) 46-. 



Johnson, W. W. Des Moines Anal. 2 (1875) 9-. 



Lucas, E. As. Fr. C. E. (1877) 159-. 



Gegenbauer, L. Wien Ak. Sb. 89 (1884) (Ab. 2) 



Piltz, . Jena. Sb. (1885) 42-. 

 Gegenbauer, L. Wien Ak. Sb. 97 (1889) 



(Ab. 2a) 374-. 



Poincare, H. C. E. 113 (1891) 819. 

 (Pomcare"'s theorem.) Stanievitch, V. C. E. 



2900 Distribution of prime 

 numbers. 



Hargreave, C. J. Ph. Mg. 35 (1849) 36-. 

 Tchebicheff, P. [1850] Liouv. J. Mth. 17 (1852) 



114 (1892) 109- ; Fschr. Mth. (1899) 190-. 

 Foussereau, G. Par. fie. Norm. A. 9 (1892) 31-. 

 Phragmen, . C. E. 114 (1892) 337-. 

 Cesdro, E. Nap. Ed. 35 (1896) 297-. 



La Vallee-Poussin, C. J. de. Brux. S. Sc. A. 



20 (1896) (Pt. 1) 100-, (Pt. 2) 183-, 281- ; 



21 (1897) (Pt. 1) xxin, 1-, 60-, (Pt. 2) 251-. 

 Koch, H. von. Stockh. Ofv. (1900) 669-. 

 Arithmetical progression containing infinity of 



primes. Lejeune-Dirichlet, G. Berl. B. 



(1837) 108- ; Liouv. J. Mth. 4 (1839) 393-. 

 . Sylvester, J. J. L. Mth. 



S. P. 4 (1871-73) 7-; C. E. 106 (1888) 1278-, 



1385-. 

 . Zignago, I. A. Mt. 21 



(1893) 47-. 

 . Speckmann, G. Arch. Mth. 



Ps. 12 (1894) 439-. 

 G. Teix. J. Sc. . Wendt, E. Crelle J. Mth. 



115 (1895) 85-. 



(Dirichlet). La Vallee- 

 Poussin, C. J. de. [1895] Brux. Mm. Cour. 

 8, 53 (1895-96) No. 6, 32 pp. 



( ). Mertens, F. Wien 



Ak. Sb. 104 (1895) (Ab. 2a) 1093-, 1158- ; 

 106 (1897) (Ab. 2a) 254-; 108 (1899) 

 (Ab. 2a) 32-. 



progressions, with difference and first term 

 mutually prime. Gegenbauer, L. Wien Ak. 

 Sb. 100 (1891) (Ab. 2a) 1018-. 



series. Sylvester, . Mess. Mth. 21 (1892) 

 1-, 87-, 192. 



Complex primes, Dirichlet' s theorem that linear 



complex function contains infinite number of. 



Mertens, F. Wien Ak. Sb. 108 (1899) (Ab. 2a) 



517-. 

 , Tchebicheff's theorems extended to. 



Poincare, H. Liouv. J. Mth. 8 (1892) 25-. 

 Composite numbers, long successions. Glaisher, 



J. W.L. [1877] Mess.Mth.,7 (1878) 102-, 171-. 



, . Lucas, E. Mess. Mth. 8 

 (1879) 81. 



Determination of primes. Bouniakowsky, V. 



[1839] St Pet. Ac. Sc. Mm. 4 (1841) 447-. 

 Divisibility of product, distribution of primes. 



Catalan, E. C. Liege S. Sc. Mm. 12 (1885) 



No. 2, 20-, 119-. 

 Enumeration of primes. Johnson, W. W. Des 



Moines Anal. 5 (1878) 7-. 

 Factors of Mobius. Koch, H. von. Stockh. 



Ofv. (1900) 659-. 

 Fermat's theorem (2 n + l prime). Baltzer, E. 



[1878] Crelle J. Mth. 87 (1879) 172. 



225 p 



