2840 Quadratic Forms of three or more Variables ; Bilinear Forms 2840 



Prime number, sum of four squares, demon- 

 strations of theorem. Catalan, E. C. Li^ge 

 S. Sc. Mm. 15 (1888) No. 1, 159-, 259. 



Primes of form 8n + 3, In + 2, 7 + 4, quadratic 

 resolution. Eisenstein, G. Crelle J. 37 (1848) 



371 + 1, quadratic resolution. Stieltjes, 



T. J. (jun.) Amst. Ak. Vs. M. 19 (1884) 105- ; 



Toul. Fac. Sc. A. 11 (1897) D, 6 pp. 

 Products of sums of squares. Degen, C. F. 



St Pet. Ac. Sc. Mm. 8 (1817-18) 207-. 

 . Graves, J. T. Ir. Ac. P. 3 



(1847) 527-. 



. Cayley,A. Ph. Mg. 4 (1852) 515-. 



. Liouville, J. Liouv. J. Mth. 2 



(1857) 351-. 



. Souillart, C. N. A. Mth. 19 



(1860) 320-. 



. Mathieu, E. [1861] Crelle J. 



60 (1862) 351-. 



. Genocchi,A. G. Mt. 2 (1864) 47-. 



. Unferdinger, F. Wien Sb. 59 



(1869) (Ab. 2) 455-. 

 . Thomson, J. J. [1877] Mess. 



Mth. 7 (1878) 73-. 

 . Studnicka, F. J. Prag. Sb. 



(1883) (Mth. Vortr.) 475-. 



. Antomari,X. C. E. 104 (1887) 566-. 



, Euler's theorem. Young, J. E. 



Ph. Mg. 30 (1847) 424-; 31 (1847) 123; Ir. 



Ac. T. 21 (1848) 311- ; Ir. Ac. P. 4 (1850) 19-. 

 , . Roberts, S. QJ. Mth. 



16 (1879) 159- ; 17 (1881) 276-. 

 Properties. Poincare, H. C. E. 89 (1879) 344-, 



897-. 

 , with tables. Pollock, (Sir) F. [1853] Phil. 



Trans. (1854) 311-. 

 Quadratic or bilinear forms, simultaneous 



transformation of two. Lipschitz, R. Berl. 



Ak. Sb. (1890) 485-. 



form of irreducible factors of binomial 

 equations. Trudi,N. A. Mt. 2 (1868-.69) 150-. 



and linear form, simultaneous reduction. 



Poincare, H. C. E. 91 (1880) 844-; Par. EC. 

 Pol. J. 56 (1886) 79-. 



forms and group-theory. Lipschitz, R. 

 Acta Mth. 10 (1887) 137-. 



of prime numbers and their powers. 

 Cauchy, A. L. C. E. 9 (1839) 473-, 519- ; 

 10 (1840) 51-, 85-, 181-, 229-. 



and linear forms of prime numbers. Oltra- 

 mare, G. Crelle J. 49 (1855) 151-. 



representations, theorem of Euler, Brioschi 

 and Genocchi. Puchta, A. Wien Ak. Sb. 

 96 (1888) (Ab. 2) 110-. 



Quaternary forms. Bazin, . Liouv. J. Mth. 



19 (1854) 215-. 



. Pepin, . Liouv. J. Mth. 6 (1890) 5-. 



, positive. Korkine, A., & Zolotareff, G. 



Mth. A. 5 (1872) 581-. 



, reduced, determinant <20, table. 

 Charve, L. C. E. 96 (1883) 773-. 



, , reduction. Charve, L. Par. EC. 

 Norm. A. 11 (1882) 119-. 



Eeduction, with proof of Seeber's theorem on 

 reduced ternary forms. Lebesgue, V. A. 

 Liouv. J. Mth. 1 (1856) 401-. 



Eepresentations of integer by certain forms, 



number. Gegenbauer, L. Wien Ak. Sb. 103 



(1894) (Ab. 2a) 115-. 

 sum of definite multiples of squares, 



mean number. Gegenbauer, L. Wien Ak. 



Sb. 93 (1886) (Ab. 2) 215-. 

 S(a,--a,-) 2 expressed as sum of n squares. 



Glaisher, J. W. L. [1878] Mess. Mth. 8 



(1879) 48. 

 Square numbers, problem. Hart, D. S. Des 



Moines Anal. 3 (1876) 81-. 

 as sums of squares. Avillez, J. F. tf 



(Visconde de Reguengo). Lisb. J. Sc. Mth. 5 



(1898) 90-. 

 , sums, theorem. Studnicka, F. J. Prag 



Sb. (1894) (Mth.-Nt.) No. 15, 8 pp. 



of odd number is difference of two triangular 

 numbers, generalisations. Henry, C. N. A. 

 Mth. 19 (1880) 517-. 



Sums of three squares. Catalan, E. C. Em. 



N. Line. At. 34 (1881) 63-, 135-. 

 Ternary forms. Hermite, C. Crelle J. 40 



(1850) 173-. 



. Bachmann, P. Crelle J. 70 (1869) 365-. 



. Picard, a. C. E. 94 (1882) 1241-. 



with complex coefficients. Fricke, R. 

 Gott. Nr. (1895) 11-. 



different determinants, comparison. 



Eisenstein, G. Berl. B. (1852) 350-. 

 , indefinite. Hermite, C. Crelle J. 47 



(1854) 307-. 

 , . Meyer, A. Crelle J. Mth. 108 



(1891) 125- ; 113 (1894) 186- ; 114 (1895) 



233-; 115 (1895) 150- ; 116 (1896) 307-. 



, orders and genera. Smith, H. J. S. 

 Phil. Trans. 157 (1867) 255-. 



, positive. Markov, V. A. Kharkov 

 Mth. S. Com. 4 (1895) 1-; Fschr. Mth. 

 (1893-94) 321-. 



, , criticism of Seeber. Anon, (vi 311) 



Crelle J. 20 (1840) 312-. 



, , reduction. Lejeune-Dirichlet, G. 

 Berl. B. (1848) 285-; Crelle J. 40 (1850) 

 209-. 



, , . Charve, L. Par. EC. Norm. A. 



9 (1880) (Suppl.) 156 pp. 

 , , . Minkowski, H. C. E. 96 (1883) 



1205-. 

 , , theorems. Eisenstein, G. Crelle J. 



35 (1847) 117-. 

 , reduction. Hermite, C. [1874] Crelle J. 



Mth. 79 (1875) 17-. 

 , transformation. Bachmann, P. [1869] 



Crelle J. 71 (1870) 296-. 



(3) = squares, problem. Matteson, J. 

 Des Moines Anal. 2 (1875) 46-. 



and quaternary forms, indefinite. Fricke, R. 

 Gott. Nr. (1893) 705-. 



Theorem. Brioschi, F. Tortolini A. 5 (1854) 



201-. 

 . Lejeune-Dirichlet, G. Liouv. J. Mth. 2 



(1857) 273-. 

 . Andre, D. Par. S. Mth. Bll. 15 (1887) 



188-. 

 Theorems. Lipschitz, R. Crelle J. 53 (1857) 



238-. 

 Theory of numbers, especially quadratic forms. 



Hermite, C. Crelle J. 40 (1850) 261-. 



211 o2 



