Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Bryce Kerr"'
Publikováno v:
Journal of the London Mathematical Society
We prove new bounds on bilinear forms with Kloosterman sums, complementing and improving a series of results by \'E. Fouvry, E. Kowalski and Ph. Michel (2014), V. Blomer, \'E. Fouvry, E. Kowalski, Ph. Michel and D. Mili\'cevi\'c (2017), E. Kowalski,
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c62723ab4a01b9fe4d00f5b830f3e1ae
https://hdl.handle.net/21.11116/0000-000D-3A6D-921.11116/0000-000D-3A6F-7
https://hdl.handle.net/21.11116/0000-000D-3A6D-921.11116/0000-000D-3A6F-7
Autor:
Bryce Kerr
Publikováno v:
Trudy Matematicheskogo Instituta imeni V.A. Steklova. 314:71-96
Пусть $q$ - натуральное число и $\chi $ - примитивный мультипликативный характер по модулю $q$. Для целых чисел $a$, взаимно простых с $q$, получена
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::346393570b8aebc442a8a8d3dc6ba162
https://doi.org/10.4213/tm4198
https://doi.org/10.4213/tm4198
Publikováno v:
Journal of Number Theory. 215:20-27
We provide an explicit estimate on the least primitive root mod p 2 . We show, in particular, that every prime p has a primitive root mod p 2 that is less than p 0.99 .
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https://explore.openaire.eu/search/publication?articleId=doi_________::a3e16d177870ba26718e2aafe5bfa3f8
https://doi.org/10.1016/j.jnt.2020.01.002
https://doi.org/10.1016/j.jnt.2020.01.002
Autor:
Matteo Bordignon, Bryce Kerr
Publikováno v:
Transactions of the American Mathematical Society. 373:6503-6527
In this paper we obtain a new fully explicit constant for the Pólya-Vinogradov inequality for squarefree modulus. Given a primitive character χ \chi to squarefree modulus q q , we prove the following upper bound: | ∑ 1 ⩽ n ⩽ N χ ( n ) | ⩽
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https://explore.openaire.eu/search/publication?articleId=doi_________::6ef295490e285b72e21a5661deee606e
https://doi.org/10.1090/tran/8138
https://doi.org/10.1090/tran/8138
Publikováno v:
Revista Matemática Iberoamericana
Motivated by recently developed interest to the distribution of $q$-arydigits of Mersenne numbers $M_p = 2^p-1$, where $p$ is prime, we estimaterational exponential sums with $M_p$, $p \leq X$, modulo a large power of afixed odd prime $q$. In turn th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::06112ad073cb2d5f7fd73f9b12e448c0
https://hdl.handle.net/21.11116/0000-0009-FF67-521.11116/0000-0009-FF69-321.11116/0000-000B-F66D-6
https://hdl.handle.net/21.11116/0000-0009-FF67-521.11116/0000-0009-FF69-321.11116/0000-000B-F66D-6
Publikováno v:
Bulletin of the Australian Mathematical Society. 100:268-280
We obtain a new sum–product estimate in prime fields for sets of large cardinality. In particular, we show that if$A\subseteq \mathbb{F}_{p}$satisfies$|A|\leq p^{64/117}$then$\max \{|A\pm A|,|AA|\}\gtrsim |A|^{39/32}.$Our argument builds on and imp
Externí odkaz:
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https://doi.org/10.1017/s0004972719000303
https://doi.org/10.1017/s0004972719000303
Publikováno v:
Illinois Journal of Mathematics. 65
Let $E_1$ and $E_2$ be elliptic curves in Legendre form with integer parameters. We show there exists a constant $C$ such that for almost all primes, for all but at most $C$ pairs of points on the reduction of $E_1 \times E_2$ modulo $p$ having equal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::168ee5d0529e29a0869dc736a5938865
https://doi.org/10.1215/00192082-9043478
https://doi.org/10.1215/00192082-9043478
Autor:
Bryce Kerr
Publikováno v:
Proceedings of the Steklov Institute of Mathematics
For an integer $$q$$ , let $$\chi$$ be a primitive multiplicative character mod $$q$$ . For integer $$a$$ coprime to $$q$$ , we obtain a bound of the form $$\bigl|\sum_{n\le N}\Lambda(n)\chi(n+a)\bigr|\le N/q^\delta$$ , $$N\ge q^{3/4+\varepsilon}$$ ,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9c30b200edf396b244053ad010e3a1c0
https://hdl.handle.net/21.11116/0000-0009-70D9-421.11116/0000-0009-708C-B21.11116/0000-0009-708E-9
https://hdl.handle.net/21.11116/0000-0009-70D9-421.11116/0000-0009-708C-B21.11116/0000-0009-708E-9
Publikováno v:
Journal of Mathematical Analysis and Applications. 459:53-81
We complement the argument of M. Z. Garaev (2009) with several other ideas to obtain a stronger version of the large sieve inequality with sparse exponential sequences of the form $\lambda^{s_n}$. In particular, we obtain a result which is non-trivia
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https://doi.org/10.1016/j.jmaa.2017.10.070
https://doi.org/10.1016/j.jmaa.2017.10.070
Autor:
Bryce Kerr
Publikováno v:
The Quarterly Journal of Mathematics. 69:729-745
We obtain a new bound for incomplete Gauss sums modulo primes. Our argument falls under the framework of Vinogradov's method which we use to reduce the problem under consideration to bounding the number of solutions to two distinct systems of congrue
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https://doi.org/10.1093/qmath/hax059
https://doi.org/10.1093/qmath/hax059