## The Rademacher Legacy to Mathematics: The Centenary Conference in Honor of Hans Rademacher, July 21-25, 1992, the Pennsylvania State UniversityThis book contains papers presented at the Hans Rademacher Centenary Conference, held at Pennsylvania State University in July 1992. The astonishing breadth of Rademacher's mathematical interests is well represented in this volume. The papers collected here range over such topics as modular forms, partitions and $q$-series, Dedekind sums, and Ramanujan type identities. Rounding out the volume is the opening paper, which presents a biography of Rademacher. This volume is a fitting tribute to a remarkable mathematician whose work continues to influence mathematics today. |

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### Contents

On Rademachers multiplier system for the classical thetafunction | 1 |

Application of Dedekind etamultipliers to modular equations | 9 |

Singularities functional equations and the circle method | 35 |

On Weyls inequality for eigenvalues | 81 |

The GL2 RankinSelberg convolution for higher level noncuspidal forms | 83 |

Congruences on the Fourier coefficients of modular forms on Γ0N | 93 |

Diagonalizing Eisenstein series IV | 107 |

Generalized Dedekind ηproducts | 119 |

On the distribution of Dedekind sums | 197 |

Wilfs conjecture and a generalization | 211 |

An elementary proof of Wilfs conjecture | 235 |

Cubic modular identities of Ramanujan hypergeometric functions and analogues of the arithmeticgeometric mean iteration | 245 |

Residue periodicity in subgroup counting functions | 265 |

Addition theorems for σfinite groups | 275 |

On sums of three integral cubes | 285 |

A note on character sums | 295 |

Vanishing coefficients in the expansion of products of RogersRamanujan type | 129 |

Schurs theorem Capparellis conjecture and qtrinomial coefficients | 141 |

Modified convergence for qcontinued fractions defined by functional relations | 155 |

A simple proof of an Aomoto type extension of the qMorris theorem | 167 |

Congruences for certain generalized Frobenius partitions modulo p3 | 183 |

Some asymptotic formulae for Ramanujans mock theta functions | 189 |

Large factors of small polynomials | 301 |

Factors of period polynomials for finite fields I | 309 |

The PhragménLindelöf theorem and modular elliptic curves | 335 |

Multidimensional beta and gamma integrals | 341 |

Rademacher calculus of variations inequalities and relative error | 359 |

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1991 Mathematics Subject 1994 American Mathematical algebra Amer American Mathematical Society analogue asymptotic automorphic forms Berndt Cartan subgroup classical cocycle cohomology colors completes the proof computation congruence conjecture consider constant term continued fractions convergence COROLLARY cusp Dedekind eta-function Dedekind sums defined denote differential Eisenstein series equation example expansion factors finite follows form of weight Fourier coefficients Frobenius partitions G. E. Andrews Gauss Gauss sums given gives Hence holomorphic identity implies inequality infinite integer invariant irreducible Lemma Let G Math Mathematics Subject Classification Mellin transform meromorphic modular forms modular group modulo multiplicative notation Note obtain order h paper Phragmén-Lindelöf theorem Poincaré series poles polynomial prime Proc proof of Theorem Proposition proved publication elsewhere q-analog q-derivative q-transportation theory quadratic Rademacher Rademacher's Ramanujan recurrence relation representations residue result root satisfies Selberg sequence singular series solutions theta functions To(N values zero