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Twisted Kloosterman sums and cubic exponential sums

Getwisteten Kloosterman Summen und kubischen exponentialen Summen

by Benoît Louvel
Doctoral thesis
Date of Examination:2008-12-15
Date of issue:2009-12-15
Advisor:Prof. Dr. Samuel James Patterson
Referee:Prof. Dr. Philippe Michel
Referee:Prof. Dr. Preda Mihailescu
Referee:Dr. Hartje Kriete
crossref-logoPersistent Address: http://dx.doi.org/10.53846/goediss-2532

 

 

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Abstract

English

In this thesis work, we study the problem of the distribution of cubic exponential sums. Using the theory of of automorphic forms, we are able to determine the asymptotic behavior of these sums. Then we use a sieve method to study the problem of the distribution of cubic sums over prime numbers.
Keywords: Analytic number theory; exponential sums; Kloosterman sums; spectral theory

Other Languages

In dieser Doktorarbeit wird das Problem der Verteilung von exponentialen Summen betrachtet. Wir studieren insbesondere die kubischen exponentialen Summen. Mit Hilfe der Theorie von automorphen Formen bestimmen wir das asymptotosche verhalten dieser Summen. Dann benützen wir eine Sieb Methode, um das Problem der Verteilung von kubischen Summen auf Primzahlen zu betrachten.
Schlagwörter: Analytische Zahlentheorie; Exponentialen Summen; Kloosterman Summen; spektrale Theory
 

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