Erratum to: “Uniform bounds for rational points on hyperelliptic fibrations”. (English) Zbl 1539.11060
From the text: There is an error in our presentation of Hooley’s upper bound [ibid. 24, No. 1, 173–204 (2023; Zbl 1539.11061), Theorem A.1]. The error arises through failing to take into account the effect of the minus sign in (A.3) in our deduction of the second displayed equation on [loc. cit., page 203]. The error is entirely the fault of the authors, the argument presented by C. Hooley [Lond. Math. Soc. Lect. Note Ser. 56, 92–122 (1982; Zbl 0488.10041)] being correct. We have elected to reproduce a corrected appendix here in full.
MSC:
| 11D45 | Counting solutions of Diophantine equations |
| 14G05 | Rational points |
| 11L40 | Estimates on character sums |
| 11N36 | Applications of sieve methods |
References:
| [1] | D. BONOLIS and T. BROWNING, Uniform bounds for rational points on hyperelliptic fi-brations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 24 (2023), 173-204. · Zbl 1539.11061 |
| [2] | P. DELIGNE, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math 43 (1974), 273-307. · Zbl 0287.14001 |
| [3] | B. DWORK, On the rationality of the zeta function of an algebraic variety, American J. Math. 82 (1960), 631-648. · Zbl 0173.48501 |
| [4] | C. HOOLEY, On exponential sums and certain of their applications, In: “Journées Arithmétiques (1980)”, J. V. Armitage (ed.), London Mathematical Society, Lecture Notes Series, Vol. 56, Cambridge Univ. Press, 1982, 92-122. · Zbl 0488.10041 |
| [5] | IST Austria Am Campus 1 3400 Klosterneuburg, Austria dantebonolide@gmail.com tdb@ist.ac.at |
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