RT Journal Article T1 On The genus of meromorphic of functions. A1 Muñoz, Vicente A1 Marco Perez, Ricardo AB We define the class of Left Located Divisor (LLD) meromorphic functions, their vertical order m(0)(f) and their convergence exponent d(f). When m0(f) <= d(f) we prove that their Weierstrass genus is minimal. This explains the phenomena that many classical functions have minimal Weierstrass genus, for example, Dirichlet series, the Gamma-function, and trigonometric functions. PB America Mathematical Society SN 1088-6826 YR 2015 FD 2015 LK https://hdl.handle.net/20.500.14352/34633 UL https://hdl.handle.net/20.500.14352/34633 LA eng NO [1] Lars V. Ahlfors, Complex analysis, 3rd ed., An introduction to the theory of analytic functions of one complex variable, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York, 1978. MR510197 (80c:30001)[2] Ralph Philip Boas Jr., Entire functions, Academic Press Inc., New York, 1954. MR0068627 (16,914f)[3] G. H. Hardy and M. Riesz, The general theory of Dirichlet’s series, Dover, 1915.[4] V. Muñoz and R. P´erez-Marco, Unified treatment of explicit and trace formulas via PoissonNewton formula, arXiv:1309.1449, 2013.[5] Laurent Schwartz, Theorie des distributions (French), Publications de l’Institut de Mathematique de l’Universit´e de Strasbourg, No. IX-X. Nouvelle ´edition, entierement corrigee, refondue et augment´ee, Hermann, Paris, 1966. MR0209834 (35 #730)[6] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Univ. Press., 4th edition, 1927. Reprinted 1962. MR0178117 (31 #2375)[7] A. H. Zemanian, Distribution theory and transform analysis, An introduction to generalized functions, with applications, 2nd ed., Dover Publications Inc., New York, 1987. MR918977 (88h:46081) NO Spanish MICINN DS Docta Complutense RD 30 abr 2024