4070 



General Periodic and Theta Functions 



4070 



Abelian functions of 2 variables, complex 

 multiplication. Wiltheiss, E. E. Mth. A. 

 21 (1883) 385-. 



. , differential equations for 

 periods. Brioschi, F. Em. B. Ac. Line. 

 Ed. 4 (1888) (Sem. 2) 341-, 429-. 



, expression in series. Brioschi, 



F. Em. E. Ac. Line. Ed. 2 (1886) (Sem. 1) 

 199-, 215-. 



, modular equations in trans- 

 formation of 3rd order. Brioschi, . Em. 



E. Ac. Line. Ed. 1 (1885) 769-. 

 , new moduli for. Brioschi, F. 



Em. E. Ac. Line. Ed. 2 (1886) (Sem. 1) 159-. 

 , transformation. Wiltheiss, . 



Crelle J. Mth. 96 (1884) 17-. 

 4 variables. Schottky, F. Crelle J. 



Mth. 102 (1888) 304-. 

 any number of variables. Klein, F. 



Gott. Nr. (1887) 515-. 



a- functions. Pascal, E. A. Mt. 17 (1889-90) 

 81-, 197- ; 18 (1890) 1-. 



, term in expansion. Schroder, J. 

 [1891] Hamb. Mth. Gs. Mt. 3 (1900) 7-. 



6 functions of 3 variables, partial differential 

 equations. Wiltheiss, E. Gott. Nr. (1889) 

 381- ; Mth. A. 38 (1891) 1-. 



integrals, reduction. Poincare, H. C. E. 

 102 (1886) 915-. 



Algebraic surfaces, class. Humbert, G. [1889] 

 Palermo Cir. Mt. Ed. 4 (1890) 54-. 



Characteristics, |>-rowed, theorem. Moore, E. H. 

 N. Y. Am. Mth. S. Bll. 1 (1895) 252-. 



Convergence of Jacobi's 6 series with Eiemann's 

 moduli. Christoffel, E. B. Ziir. Vjschr. 41 

 (1896) (Festschr., Th. 2) 3-. 



Differential equations, integrals of which 

 are Abelian functions of 1st kind, two 

 systems. Caspary,F. C. E. 112 (1891) 1305-. 



of theta functions, formation. Caspary, 



F. C. E. 112 (1891) 1120-. 



Doubly periodic functions, uniform, behaviour 



at essential singularities. Appell, P. C. E. 



94 (1882) 936-. 

 Elliptic Abelian functions of 4 variables. Schott* 



ky, F. Crelle J. Mth. 108 (1891) 147-, 193-. 

 Function, single- valued, of n variables cannot 



have more than 2n periods. Riemann, [G. 



F.-] B. Crelle J. 71 (1870) 197-. 

 Functions of 3rd kind. Tichomandrickij, M. 



A. Kharkov Mth. S. Com. 5 (1896?) 182- ; 



Fschr. Mth. (1896) 360. 



with 4 pairs of periods. Humbert, G. C. 

 E. 130 (1900) 483-. 



2 real periods, class. Staude, 0. Mth. 



A. 29 (1887) 468-. 



of 2 variables analogous to modular func- 

 tions. Picard, E. Acta Mth. 2 (1883) 114-. 



Weierstrass's elliptic func- 

 tions. Pokrovskij, P. M. Bee. Mth. (Moscou) 

 18 (1896) 598-; Fschr. Mth. (1896) 360. 



with 3 or 4 pairs of periods. 

 Appell, P. C. B. 90 (1880) 174-. 



several pairs of periods. Appell, 



P. C. E. 110 (1890) 181-. 



and 4 periods, inverses of Abelian 



integrals of 1st class. Rosenhain, G. [1846] 

 Par. Mm. Sav. Etr. 11 (1851) 361-. 



Functions of n variables admitting 2n systems 



of periods, Eiemann's theorem. Picard, E., 



& Poincare, H. C. E. 97 (1883) 1284-. 

 Hyperabelian functions and surfaces represent- 



ablebythem. Humbert, G. C. B. 129 (1899) 



667. 

 Inversion problem. Elliot, Z. C. E. 90 



(1880) 1466-. 

 , Jacobi's. Noether, M. Erlang. Ps. Md. 



S. Sb. 16 (1884) 88-. 

 Jacobian functions of fcth order of 2 variables. 



Witting, A. Mth. A. 29 (1887) 157-. 

 3 variables. Frobenius, G. Crelle J. 



Mth. 105 (1889) 35-. 

 several variables. Weierstrass, C. T. 



W. Bll. Sc. Mth. As. 6 (1882) (Pt. 1) 136-. 

 Lame's differential equation, generalisation. 



GrSnwall, H. Stockh. Ofv. (1898) 357-. 

 Linear equations integrable with, the help of 



X m (x, y). Appell, P. Par. EC. Norm. A. 5 



(1888) 211-. 

 Periodic functions, 2w-ply. Wirtinger, W. 



Mh. Mth. Ps. 6 (1895) 69- ; 7 (1896) 1-. 

 , , application to total differential equa- 

 tions. Gronwall, H. Stockh. Ofv. (1896) 



295-; Fschr. Mth. (1896) 285-. 

 , , of r variables. Weierstrass, C. T. 



W. Crelle J. Mth. 89 (1880) 1-. 

 , special 4-ply. Roch, G. Z. Mth. Ps. 



11 (1866) 463-. 

 of 2 variables. Appell, P. C. B. Ill 



(1890) 636- ; Liouv. J. Mth. 7 (1891) 157-. 

 , n variables. Puiseux, V. C. E. 43 



(1856) 321-. 



, , demonstration of a leading 



theorem. Weierstrass, C. T. W. Berl. Ak. 

 Mb. (1876) 680-. 



, , most general uniform and 2n- 



ply. Weierstrass, C. Berl. Mb. (1869) 853-. 

 Periodicity, general, theory. Rausenberger, 0. 



Mth. A. 18 (1881) 379-. 

 Periods of double integrals. Picard, E. C. B. 



102 (1886) 349-. 

 . Poincare, H. C. B. 125 (1897) 



995-. 

 of algebraic functions. Picard, E. 



C. B. 125 (1897) 1068-. 

 , calculation. Picard, E. C. B. 



102 (1886) 410-. 



and two-dimensional cycles on 

 algebraic surfaces. Picard, E. C. B. 126 

 (1898) 1457-. 



uniform 2n-ply periodic functions. Hur- 



witz,A. [1882] Crelle J. Mth. 94 (1883) 1-. 



Potential, properties ; and Abelian functions. 

 Poincare, H. Acta Mth. 22 (1899) 89-. 



Quadruply periodic expressions. Picard, E. 

 Par. S. Mth. Bll. 17 (1889) 131-. 



depending on 2 variables. Picard, E. 



C. E. 108 (1889) 557-. 



. Appell, P. C. E. 108 



(1889) 607-. 



functions of 2nd kind, systems of diffe- 

 rential equations satisfied by. Krause, M. 

 C. E. 126 (1898) 1086-, 1489-, 1618- ; 127 

 (1898) 91- ; A. Mt. 1 (1898) 265-. 



336 



