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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 11L: Exponential sums and character sums

Introduction

History

Applications and related fields

Subfields

• 11L03: Trigonometric and exponential sums, general
• 11L05: Gauss and Kloosterman sums; generalizations
• 11L07: Estimates on exponential sums
• 11L10: Jacobsthal and Brewer sums; other complete character sums
• 11L15: Weyl sums
• 11L20: Sums over primes
• 11L26: Sums over arbitrary intervals
• 11L40: Estimates on character sums
• 11L99: None of the above, but in this section

Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

• Karatsuba, A. A., "I. M. Vinogradov's method of trigonometric sums", International conference on analytical methods in number theory and analysis (Moscow, 1981). Trudy Mat. Inst. Steklov. 163 (1984), 97--103.
• Huxley, M. N., "Exponential sums after Bombieri and Iwaniec", Journées Arithmétiques, 1989 (Luminy, 1989). Astérisque No. 198-200 (1991), 165--175 (1992).

For a survey see Vaughan, R. C.: "Adventures in arithmetick, or: how to make good use of a Fourier transform", Math. Intelligencer 9 (1987), no. 2, 53--60. MR88g:11002.

Software and tables

Other web sites with this focus

Selected topics at this site

• Simplifying trigonometric sums with symmetry.
• Calculating a product in Z[exp(2 pi i)/p].
• Quadratic Gauss sum