4050 



Modular Equations and Functions 



4050 



Hermite's ^-function, linear transformation. 



Konigsberger, . Mth. A. 3 (1871) 1-. 

 Integral occurring in Cauchy's transformation 



of elliptic integral. Lerch, M. D. Nf. Vh. 



(1894) (Th. 2, Halfte 1) 8-. 

 Jacobian functions. Frobenius, G. Crelle J. 



Mth. 97 (1884) 16-, 188-. 

 , generalisation of formula. Hoppe, R. 



Arch. Mth. Ps. 70 (1884) 400-. 

 Kleinian functions of 3rd family, generalisation. 



Cassel, G. Stockh. Ofv. (1890) 237- ; Fschr. 



Mth. (1890) 410. 

 Landen's substitution. Koldcek, F. Casopis 



18 (1889) 21- ; Fschr. Mth. (1889) 495. 

 Linear equation connecting complete function 



of 1st kind with modulus. Tannery, J. C. 



B. 86 (1878) 811-. 

 . Goursat, E. 



Par. S. Mth. Bll. 10 (1882) 44-. 

 Modular correspondences of 7th kind. Fricke, 



E. Gott. Nr. (1892) 272-. 



Modular equations, 



Schroter, H. E. Crelle J. 58 (1861) 378-. 



Jordan, C. C. E. 66 (1868) 308-. 



Smith, H. J. S. Bm. B. Ac. Line. Mm. 1 



(1877) 136-. 



Klein, C. F. Mil. I. Lomb. Bd. 12 (1879) 21-. 

 Pick, G. Wien Ak. Sb. 91 (1885) (Ab. 2) 138-. 

 Russell, R. [1890] L. Mth. S. P. 21 (1891) 351-. 

 Brioschi, F. Bm. B. Ac. Line. Bd. 2 (1893) 



(Sem. 2) 185- ; 5 (1896) {Sem. 2) 333-. 

 Pierpont, J. N. Y. Am. Mth. S. Bll. 3 (1897) 



279-. 

 and application to theory of numbers. Krause, 



M. Mth. A. 12 (1877) 419-. 

 class. Brioschi, F. C. B. 112 (1891) 28-. 

 and curves, singularities. Smith, H. J. S. L. 



Mth. S. P. 9 (1877-78) 242-. 

 of 8th degree, new form. Brioschi, F. Am. 



J. Mth. 13 (1891) 381-. 

 , property of reduced form. Brioschi, 



F. Bm. E. Ac. Line. Bd. 1 (1885) 514-, 583-. 

 , reduction. Hermite, C. Tortolini 



A. 2 (1859) 59-. 



12th degree, resolvent of llth degree. Klein, 

 C. F. Bm. B. Ac. Line. T. 3 (1879) 177-. 



discriminants. Krause, M. Mth. A. 8 (1875) 



539- ; 9 (1876) 554-. 

 equations analogous to. Brioschi, F. C. B. 



47 (1858) 337-. 



. Joubert, P. C. B. 47 (1858) 341-. 



form in transformation of 3rd order. Cayley, 



A. Mess. Mth. 12 (1883) 173-. 



Galois' s group. Gierster, J. Leip. Mth. Ps. 



B. 37 (1885) 291- ; Mth. A. 26 (1886) 309-. 

 , sub-groups in case of a transformation 



of prime degree. Gierster, J. Mth. A. 18 



(1881) 319-. 

 irrational. Fiedler, E. W. Ziir. Vjschr 30 



(1885) 129-. 

 reduction. Betti, E. Tortolini A. 4 (1853) 81-. 



of degree. Sylow, L. [1870] Christiania 

 F. 13 (1871) 387-. 



resolution, cases. Morera, G. Mil. I. Lomb. 

 Bd. 18 (1885) 629-. 



theory. Schroter, H. E. Liouv. J. Mth. 3 



(1858) 258-. 

 . Hermite, C. C. B. 48 (1859) 940-, 1079-, 



1095- ; 49 (1859) 16-, 110-, 141-. 

 , algebraic proofs. Igel, B. Mh. Mth. Ps. 3 



(1892) 349-. 

 K \ - K'\'. Russell, R. [1887] L. Mth. S. P. 19 



(1889) 90-. 



MODULAB FUNCTIONS. 



Klein, C. F. [1879] Munch. Ak. Sb. 10 (1880) 



89-. 



Rausenberger, 0. Mth. A. 20 (1882) 45-. 

 Wirtinger, W. Mh. Mth. Ps. 1 (1890) 429-. 

 Cayley, A. Mth. A. 47 (1896) 1-. 

 Weber, H. Mth. A. 47 (1896) 6-. 

 Lewicki, W. Prace Mt.-Fiz. 8 (1897) 5-. 

 demonstration of Hermite's transformation 



tables. Schlqfli,L. Crelle J. 72 (1870) 360-. 

 functions akin to. Stouff, X. Toul. Fac. Sc. 



A. 5 (1891) C, 16 pp. 

 and Gauss's theory of arithmetico-geometric 



mean. Schlesinger, L. Berl. Ak. Sb. (1898) 



346-. 



integrals. Gudermann, C. Crelle, J. 18 

 (1838) 1-, 142-, 220-, 303- ; 19 (1839) 45-, 

 119-, 244- ; 20 (1840) 62-, 103- ; 21 (1840) 

 240- ; 23 (1842) 301- ; 25 (1843) 281- ; 41 

 (1851) 93-; [Latin version with preface 

 and annotations by J. F. Stader] Tortolini 



A. 2 (1851) 557- ; 3 (1852) 442- ; 5 (1854)81-. 



invariants, differential equations. Scheibner, 

 W. Leip. Mth. Ps. B. 41 (1889) 331-. 



of lowest degrees. Klein, F. Leip. Mth. Ps. 



B. 37 (1885) 70-. 



and multiplicator equations of 1st degree, 



foundations of theory. Hurwitz, A. Mth. 



A. 18 (1881) 528-. 

 representation by infinite products. Mangoldt, 



H. von. Gott. Nr. (1885) 313-. 

 , and extension to their functions. 



Mangoldt, H. von. Gott. Nr. (1886) 1-. 

 special subgroups. Fricke, R. Mth. A. 31 



(1888) 227-. 

 theory. Dienger, J. Grunert Arch. 11 (1848) 



395- ; 13 (1849) 1- ; 21 (1853) 344- ; 22 (1854) 



362-. 



. Dedekind,R. Crelle J. Mth. 83 (1877) 265-. 

 X<a. Cayley, A. C. E. 116 (1893) 1339-. 



Modular group. Lewicki, W. Mh. Mth. Ps. 



11 (1900) 118-. 

 , sub-groups of llth class. Rougier, J. 



Mars. Fac. Sc. A. 6 (1897) Fasc. 1, 112 pp. 



groups, automorphic. Fricke, R. Gott. Nr. 

 (1896) 91-. 



relations, new. Brioschi, F. [1866] Nap. 

 At. Ac. 3 (1866-68) (No. 2) 16 pp. 



transformation of degree p. Frattini, G. 

 Bm. B.Ac. Line. Ed. 1 (1885) 142-, 166-, 884. 



5th order. Invariant theory of its 



sextic equation. Gordan, P. A. Mt. 1 

 (1867-68) 367-. 



transformations, application of a theorem of 

 Abel to solution of a geometrical problem. 



, Roberts, W. C. E. 58 (1864) 709-. 



326 



