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This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Moebius function, Euler's totient function, the Riemann zeta function and the Riemann Hypothesis.

## Paul Pollack

Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Halberstam, H.

On Gaps between Squarefree Numbers. Some Arithmetical Semigroups. Fraenkel, H. Porta, K. Norms in Arithmetic Progressions. Modular Integrals and Their Mellin Transforms.

## NUMBER THEORY BOOKS,

The Coefficients of Cyclotomic Polynomials. Best Possible Results on the Density of Sumsets. Some Powers of The Euler Product. Diagonalizing Eisenstein Series.

Some Binary Partition Functions. On the Minimal Level of Modular Forms. Back Matter Pages About this book Introduction On April , , over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory.

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For fifteen of these years, he served as head of the mathematics department. Delange, P.

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