Detail 2-adic modular forms of minimal slope Bibliografi Author: Mazur, Barry (Advisor); Emerton, Matthew James Topik: MATHEMATICS Bahasa: (EN )    ISBN: 0-591-85438-4     Penerbit: Harvard University Press     Tahun Terbit: 1998     Jenis: Theses - Dissertation Fulltext: 9832360.pdf (0.0B; 3 download) Abstract Let $[/cal W]$ denote the space of 2-adic weights, and let $P(/kappa, T)$ denote the characteristic power series of the completely continuous operator $U/sb2$ acting on the space of overconvergent 2-adic cusp forms of weight $/kappa$. We construct a map $/kappa(u)$ from the 2-adic rigid analytic annulus $[/cal A]$ defined by $1 > /vert u/vert /ge /vert 64/vert$ to the space of 2-adic weights $[/cal W]$, such that for any $/kappa /in [/cal W]$(C$/sb2),$ the points of $u /in [/cal A]$(C$/sb2)$ lying over $/kappa$ are precisely the reciprocal zeroes of $P(/kappa, T)$ of minimal slope. Furthermore, we construct a family f(u) of overconvergent 2-adic cusp forms of weight $/kappa(u)$ rigid analytically parameterized by $[/cal A]$, such that for any $u /in [/cal A]$(C$/sb2),$ the cusp form f(u) is the unique normalized overconvergent 2-adic Hecke eigenform of weight $/kappa$ whose U-eigenvalue is equal to u. The construction is explicit, and allows us to prove precise congruences between the eigenforms f(u) for different values of u, as well congruences between the family of cusp forms f(u) and the family of Eisenstein series $E/sbsp[/kappa(u)][*].$ Opini Anda Klik untuk menuliskan opini Anda tentang koleksi ini! Lihat Sejarah Pengadaan  Konversi Metadata   Kembali

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