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- W4230542962 abstract "[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This thesis is focus on the methods of exponential sums and sieve methods applying to distribution of primes numbers in several forms, such as Piatetski-Shapiro primes, Beatty sequences, almost primes and primes in arithmetic progression. In the end, we also think about the classical problem in Burgess bound. We begin by explaining the importance of the methods of exponential sums. Together with sieve methods, we investigate the Piatetski-Shapiro primes from almost primes and the intersection between Piatetski-Shapiro primes and Betty sequences. Above all, we study primes in several forms from a thin integer set. We also study the distribution of consecutive prime numbers from two Beatty sequences by an assumption of a well-known conjecture. Finally, we turn to the methods of character sums and the problem of the least quadratic nonresidue. We improve the best known bound by changing the arbitrary small constant into a reciprocal of an infinite function. Possible future work is also discussed in the thesis." @default.
- W4230542962 created "2022-05-11" @default.
- W4230542962 creator A5085676958 @default.
- W4230542962 date "2021-04-14" @default.
- W4230542962 modified "2023-09-29" @default.
- W4230542962 title "Exponential sums, character sums, sieve methods and distribution of prime numbers" @default.
- W4230542962 doi "https://doi.org/10.32469/10355/61884" @default.
- W4230542962 hasPublicationYear "2021" @default.
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