Goss, David \(\pi\)-adic Eisenstein series for function fields. (English) Zbl 0422.10020 Compos. Math. 41, 3-38 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 42 Documents MSC: 11F85 \(p\)-adic theory, local fields 11F11 Holomorphic modular forms of integral weight 14K15 Arithmetic ground fields for abelian varieties 14G20 Local ground fields in algebraic geometry 11R58 Arithmetic theory of algebraic function fields Keywords:pi-adic Eisenstein series; q-expansion; double cusp forms; Hecke operators; dimensions; genera of moduli curves Citations:Zbl 0321.14014; Zbl 0388.10020 PDF BibTeX XML Cite \textit{D. Goss}, Compos. Math. 41, 3--38 (1980; Zbl 0422.10020) Full Text: Numdam EuDML OpenURL References: [1] P. Deligne and D. Husemoller : Survey of Drinfeld Modules (to appear). · Zbl 0627.14026 [2] V.G. Drinfeld : Elliptic Modules (Russian) . Math. Sbornik, 94 (1974) 594-627. (English translation, Math USSR, Sbornik, Vol. 23 (1974) No. 4). · Zbl 0321.14014 [3] D. Goss : von Staudt For F q[T] , Dec. 1978, Duke Math. Journal. · Zbl 0404.12013 [4] D. Hayes : Explicit Class Field Theory in Global Function Fields (Preprint). · Zbl 0292.12018 [5] P. Deligne and M. Rappoport , Les Schémas de Modules de Courbes Elliptiques in Modular Function of One Variable II . Springer-Verlag, Lecture Notes #349 (1973) 55-316. · Zbl 0281.14010 [6] P. Deligne : Formes Modulaires et Représentations de GL(2), in Modular Functions of One Variable II . Springer-Verlag, Lecture Notes #349 (1973) 55-105. · Zbl 0271.10032 [7] E. Hecke : Mathematische Werke . Vanderhoeck and Ruprecht (1970). · Zbl 0205.28902 [8] N. Katz : P-adic Properties of Modular Schemes and Modular Forms, in Modular Functions of One Variable III . Springer-Verlag, Lecture Notes #350 (1973) 69-190. · Zbl 0271.10033 [9] S. Lang : Elliptic Functions . Addison-Wesley (1973). · Zbl 0316.14001 [10] A. Ogg : Modular Forms and Dirichlet Series , Benjamin (1969). · Zbl 0191.38101 [11] A. Ogg : Rational Points on Certain Elliptic Modular Curves . Proc. Symp. Pure Math., 24 AMS, Providence (1973) 221-231. · Zbl 0273.14008 [12] J.-P. Serre : A course in Arithmetic , Springer-Verlag (1973). · Zbl 0256.12001 [13] G. Shimura : Introduction to the Arithmetic Theory of Automorphic Functions . Publ. Math. Soc. Japan, No 11, Tokyo-Princeton (1971). · Zbl 0221.10029 [14] H. Grauert : L.L. Gerritzen , Die Azyklizität der affinoiden Überdeckungen , in Global Analysis , Univ. of Tokyo Press (1969) 159-184. · Zbl 0197.17303 [15] R. Kiehl : Der Endlichkeitsatz für eigenliche Abbildungen in der nichtarchimedischen Funktionen Theorie . Invent. Math. 2 (1967) 191-214. · Zbl 0202.20101 [16] R. Kiehl : Theorem A and Theorem B in der nichtarchimedischen Funcktionen Theorie . Invent. Math. 2 (1967) 256-273. · Zbl 0202.20201 [17] M. Raynaud : Géométrie Analytic Rigid d’aprés Tate, Kiehl , Bull. Soc. Math. France. Memoire 39-40 (1974) 319-327. · Zbl 0299.14003 [18] M. Raynaud : Unpublished Notes . [19] A. Robert : Elliptic Curves , Springer-Verlag, Lecture Notes #326 (1973) II.70-II.85. · Zbl 0256.14013 [20] J. Tate : Rigid Analytic Space , Inventiones Math 12 (1971) 257-258. · Zbl 0212.25601 [21] A. Altman and S. Kleiman : Introduction to Grothendieck Duality Theory . Springer-Verlag, Lecture Notes #146 (1970). · Zbl 0215.37201 [22] C. Curtis and I. Reiner : Representation Theory of Finite Groups and Associative Algebras . Interscience (1962) 144-154. · Zbl 0131.25601 [23] A. Fröhlich : Formal Groups . Springer-Verlag, Lecture Notes #74 (1968). · Zbl 0177.04801 [24] A. Grothendieck : Éléments de Géométrie Algébrique III (rédigé avec la collaboration de J. Dieudonné) . Publ. Math. IHES (1961). | [25] D. Mumford : Geometric Invariant Theory . Springer-Verlag (1965). · Zbl 0147.39304 [26] D. Mumford : Varieties Defined by Quadratic Equations . C.I.M.E. (1969) 31-94. · Zbl 0198.25801 [27] J.P. Serre : Cohomologie des Groupes Discrets, in Prospects in Mathematics . Princeton University Press (1971) 77-169. · Zbl 0235.22020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.