Exponential sums over cubes of primes in short intervals and its applications
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DOI: 10.1007/s00209-020-02649-8
Abstract: In this paper, we treat the estimate on exponential sums over cubes of primes in short intervals, and improve a previous bound of Kumchev (in: Number Theory: Arithmetic in Shangri-La (Proc. China-Japan Seminar Number Theory),… read more here.
Keywords: exponential sums; cubes primes; sums cubes; intervals applications ... See more keywords
On Cubic Exponential Sums and Gauss Sums
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DOI: 10.1007/s10958-018-4037-0
Abstract: Let eq be a nontrivial additive character of a finite field ????q of order q ≡ 1(mod 3) and let ψ be a cubic multiplicative character of ????q, ψ(0) = 0. Consider the cubic Gauss… read more here.
Keywords: sum; exponential sums; cubic exponential; psi right ... See more keywords
Ramanujan graphs and exponential sums over function fields
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DOI: 10.1016/j.jnt.2020.05.010
Abstract: We prove that $q+1$-regular Morgenstern Ramanujan graphs $X^{q,g}$ (depending on $g\in\mathbb{F}_q[t]$) have diameter at most $\left(\frac{4}{3}+\varepsilon\right)\log_{q}|X^{q,g}|+O_{\varepsilon}(1)$ (at least for odd $q$ and irreducible $g$) provided that a twisted Linnik-Selberg conjecture over $\mathbb{F}_q(t)$ is true. This… read more here.
Keywords: sums function; ramanujan graphs; graphs exponential; exponential sums ... See more keywords
BOUNDS FOR TRIPLE EXPONENTIAL SUMS WITH MIXED EXPONENTIAL AND LINEAR TERMS
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DOI: 10.1017/s0004972718000205
Abstract: We establish bounds for triple exponential sums with mixed exponential and linear terms. The method we use is by Shparlinski [‘Bilinear forms with Kloosterman and Gauss sums’, Preprint, 2016, arXiv:1608.06160] together with a bound for… read more here.
Keywords: triple exponential; mixed exponential; exponential sums; sums mixed ... See more keywords
The Covering Method for Exponential Sums and Some Applications
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DOI: 10.1090/noti2073
Abstract: DOI: https://doi.org/10.1090/noti2073 elementary and intuitive way to estimate or compute the pdivisibility of exponential sums, which is particularly convenient in the applications. The covering method allows us to determine solvability of systems of polynomial equations,… read more here.
Keywords: exponential sums; sums applications; method exponential; applications covering ... See more keywords
Restriction of Exponential Sums to Hypersurfaces
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DOI: 10.1093/imrn/rnab278
Abstract: We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale… read more here.
Keywords: restriction exponential; sums hypersurfaces; exponential sums;
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
THE TSUKANO CONJECTURES ON EXPONENTIAL SUMS
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DOI: 10.18910/76672
Abstract: We prove three conjectures of Tsukano about exponential sums stated in his Master’s thesis written at Osaka University. These conjectures are variations of earlier conjectures made by Lee and Weintraub which were first proved by… read more here.
Keywords: tsukano conjectures; exponential sums; conjectures exponential;