Lectures on Modular FormsPrinceton University Press, 21 mrt 1962 - 86 pagina's New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H. C. Gunning's book surveys techniques and problems; only the simpler cases are treated-modular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone. |
Inhoudsopgave
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III | 8 |
IV | 10 |
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VII | 21 |
VIII | 23 |
XIV | 44 |
XV | 49 |
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Veelvoorkomende woorden en zinsdelen
algebra branch schema Chapter compact Riemann surface compact subsets complete set congruence subgroup converges absolutely uniformly Corollary cusp form defined differential form dxdy Eisenstein series elliptic f(Tz finite number finite parabolic fixed point form of weight Fourier coefficients Fourier expansion fundamental domain G₂ genus group G H mod h(Tz Hecke Hecke Operators holomorphic incongruent integers c,d Jacobi inversion formula Let f(z linear fractional transformations M₁ matrix meromorphic function mod pi modular group modulo normal subgroup notation obtain pair c,d parabolic points parabolic vertices Petersson inner product Poincaré series points equivalent positive definite Proof quadratic form S-transform S₁ series of weight set of coset shows space of cusp space of modular subgroup of index subsets of H term Theorem uniformly on compact unrestricted modular form upper half plane vanishes vertex zero
Verwijzingen naar dit boek
Modular Functions and Dirichlet Series in Number Theory Tom M. Apostol Geen voorbeeld beschikbaar - 1997 |