SUBJECT

Title

Exponential sums in number theory

Type of instruction

lecture

Level

master

Part of degree program
Credits

3

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Additive and multiplicative characters, their connection, applications. Vinogradov's lemma and its dual. Gaussian sums. The Pólya-Vinogradov inequality. Estimate of the least quadratic nonresidue. Kloosterman sums. The arithmetic and character form of the large sieve, applications. Irregularities of distribution relative to arithmetic progressions, lower estimate of character sums. Uniform distribution. Weyl's criterion. Discrepancy. The Erdős-Turán inequality. Van der Corput's method.

Readings
  • I. M. Vinogradov: Elements of number theory

  • L. Kuipers, H. Niederreiter: Uniform Distribution of Sequences.

  • S. W. Graham, G. Kolesnik: Van der Corput’s Method of Exponential Sums.

  • H. Davenport: Multiplicative Number Theory.