## Number Theory and Its Applications"Addresses contemporary developments in number theory and coding theory, originally presented as lectures at summer school held at Bilkent University, Ankara, Turkey. Includes many results in book form for the first time." |

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### Contents

Mehpare Bilhan Middle East Technical University Ankara | 21 |

Some Function Field Estimates with Applications | 23 |

Topics in Analytic Number Theory | 47 |

Cohen University of Glasgow Glasgow Scotland | 64 |

The Sieve Method | 65 |

Toronto Ontario Canada | 107 |

A Remark on the Nonexistence of Generalized Bent Functions | 109 |

Cardiff Wales | 119 |

The Mahler Measure of Polynomials | 171 |

Nesterenko Moscow State University Moscow Russia | 183 |

Heights of Algebraic Points | 185 |

Schmidt University of Colorado at Boulder | 225 |

Fibre Products Character Sums and Geometric Goppa Codes | 227 |

Vinogradovs Method and Some Applications | 261 |

From Simultaneous Approximations to Algebraic Independence | 283 |

A Survey of Results on Primes in Short Intervals | 307 |

### Common terms and phrases

abelian extension absolute value Acta Arith algebraic closure algebraic independence algebraic integer algebraic number applications arithmetic progressions assume asymptotic bent function Brun's character coefficients completes the proof complex number conjecture constant coprime Corollary cosets curve cusp defined degree denote Dirichlet distinct divisor elements equations estimate example exists fibre products field Fq finite field formula function fields Galois given Goppa codes Hence holds homogeneous implies inequality irreducible Iwaniec lectures Lemma linear linear codes lower bound Math minimal polynomial multiplicative naive height nontrivial notation Number Theory obtain Ozbudak parameters points positive integer prime factors prime ideals prime number prime number theorem prime polynomials primitive problem proof of Theorem Proposition proved ramification rational real numbers root of unity satisfying Selberg's sequence sieve method simultaneous approximation squarefree Stepanov sufficiently large Suppose term Theorem 9 transcendence transcendental number upper bound variables vector Vinogradov zeros