In this thesis we prove several results in analytic number theory.
1. We show that there exist 3-digit palindromic primes in base b for a set of b having density 1 and that if b is sufficiently large then there is a $3$-digit palindrome in base b having precisely two prime factors.
2. We prove various estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski a...Expand abstract
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- Oxford University, UK
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- Alastair James Irving
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Topics in analytic number theory
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