Contents Preface Real Hilbertianity and the field of totally real numbers MICHAEL D. FRIED, DAN HARAN, AND HELMUT VOLKLEIN 1 Galois groups with prescribed ramification DAVID HARBATER 35 Note on the zeros of p-adic £-functions TAUNO METSANKYLA 61 La fonction L p-adique de Kubota-Leopoldt BERNADETTE PERRIN-RIOU 65 Supersingular p-adic height pairings on elliptic curves ANDREW PLATER 95 Fields of definition of abelian varieties with real multiplication KENNETH A. RIBET 107 p-adic interpolation of half-integral weight modular forms ADRIANA SOFER 119 A-adic modular forms of half-integral weight and a A-adic Shintani lifting GLENN STEVENS 129 The non-existence of certain Galois extensions of Q unramified outside 2 JOHN TATE 153 Iwasawa theory and cyclotomic function fields DINESH S. THAKUR 157 Slopes of modular forms DOUGLAS L. ULMER 167 On the Taylor coefficients of theta functions of CM elliptic curves FERNANDO RODRIGUEZ VILLEGAS 185 Torsion groups of elliptic curves over cubic and certain biquadratic number fields HORST G. ZIMMER vii 203

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