Long large character sums
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DOI: 10.1112/mtk.12116
Abstract: In this paper, we prove a lower bound for $\underset{\chi \neq \chi_0}{\max}\bigg|\sum_{n\leq x} \chi(n)\bigg|$, when $x= \frac{q}{(\log q)^B}$. This improves on a result of Granville and Soundararajan for large character sums when the range of… read more here.
Keywords: character sums; chi; long large; character ... See more keywords
LARGE VALUES OF FOR TH ORDER CHARACTERS AND APPLICATIONS TO CHARACTER SUMS
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DOI: 10.1112/s0025579316000164
Abstract: For any given integer $k\geqslant 2$ we prove the existence of infinitely many $q$ and characters $\unicode[STIX]{x1D712}\,(\text{mod}\;q)$ of order $k$ such that $|L(1,\unicode[STIX]{x1D712})|\geqslant (\text{e}^{\unicode[STIX]{x1D6FE}}+o(1))\log \log q$ . We believe this bound to be the best… read more here.
Keywords: character sums; unicode stix; order; stix x1d712 ... See more keywords
On a Certain Quadratic Character Sums of Ternary Symmetry Polynomials mod p
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DOI: 10.1155/2021/5572835
Abstract: In this article, we are using the elementary methods and the properties of the classical Gauss sums to study the calculating problem of a certain quadratic character sums of a ternary symmetry polynomials modulo and… read more here.
Keywords: sums ternary; quadratic character; character sums; ternary symmetry ... See more keywords
On One Kind of Character Sums and Its Applications
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DOI: 10.1155/2023/9491445
Abstract: The aim of this study is to use analytic methods and the properties of character sums to calculate the number of solutions to certain congruence equations modulo an odd prime. Formulas for the exact number… read more here.
Keywords: sums applications; kind character; character sums; one kind ... See more keywords
On the two-term exponential sums and character sums of polynomials
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DOI: 10.1515/math-2019-0107
Abstract: Abstract The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character… read more here.
Keywords: exponential sums; sums polynomials; character sums; two term ... See more keywords