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Problems with power-free numbers and Piatetski-Shapiro sequences

Bongiovanni, Alex
http://orcid.org/0000-0001-7124-4764
http://rave.ohiolink.edu/etdc/view?acc_num=kent1618331559201676

Abstract Details

2021, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Several problems with power-free numbers and Piatetski-Shapiro sequences are investigated. Two of these problems are divisor sums for which an asymptotic formula is proved, one where the divisors are restricted to be k-free and l-free, and the other where one divisor belongs to a Piatetski-Shapiro sequence. In another problem an asymptotic formula is proved for the number of consecutive power-free numbers in a Piatetski-Shapiro sequence. Finally, several approximations to Conjecture H of Hardy and Littlewood using Piatetski-Shapiro sequences are investigated.
Gang Yu (Advisor)
Morley Davidson (Committee Member)
Ulrike Vorhauer (Committee Member)
Xiang Lian (Committee Member)
75 p.
Mathematics
exponential sums; analytic number theory; power-free numbers; piatetski-shapiro sequences; divisor sums

Recommended Citations

Citations

  • Bongiovanni, A. (2021). Problems with power-free numbers and Piatetski-Shapiro sequences [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1618331559201676

    APA Style (7th edition)

  • Bongiovanni, Alex. Problems with power-free numbers and Piatetski-Shapiro sequences. 2021. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1618331559201676.

    MLA Style (8th edition)

  • Bongiovanni, Alex. "Problems with power-free numbers and Piatetski-Shapiro sequences." Doctoral dissertation, Kent State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1618331559201676

    Chicago Manual of Style (17th edition)

kent1618331559201676
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This open access ETD is published by Kent State University and OhioLINK.