Results 41 to 50 of about 108 (105)
Lattices in function fields and applications
Mathematika, Volume 71, Issue 2, April 2025.Abstract In recent decades, the use of ideas from Minkowski's Geometry of Numbers has gained recognition as a helpful tool in bounding the number of solutions to modular congruences with variables from short intervals. In 1941, Mahler introduced an analogue to the Geometry of Numbers in function fields over finite fields.
Christian Bagshaw, Bryce Kerr
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ESC Heart Failure, Volume 11, Issue 6, Page 4046-4060, December 2024.In our study, we analyzed data from 17 studies on different cardiac resynchronization therapy optimization techniques within a network meta‐analysis. Dynamic algorithms showed superior outcomes, including higher echocardiographic response rates, lower heart failure hospitalization rates, and greater six‐minute walk test improvement compared to ...
Előd‐János Zsigmond +9 more
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A note on the mean value of the general Kloosterman sums [PDF]
Czechoslovak Mathematical Journal, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the general Kloosterman sum and its fourth power mean
Journal of Number Theory, 2004 Let \(q \geq 3\) be a positive integer and let \(\chi\) denote a Dirichlet character mod \(q\). For any integers \(m\) and \(n\), the general Kloosterman sum \(S(m ,n , \chi ; q)\) is defined as follows: \[ S(m,n, \chi ; q) = \mathop{{\sum}^*}_{a=1}^q \chi(a) e\left(\frac {ma+n \overline{a}}{q} \right), \] where \(e(y) = e^{2 \pi i y}\) and \(\sum ...
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, 2009 In this paper, we construct two binary linear codes associated with multi-dimensional and $m -$multiple power Kloosterman sums (for any fixed $m$) over the finite field $\mathbb{F}_{q}$. Here $q$ is a power of two. The former codes are dual to a subcode of the binary hyper-Kloosterman code. Then we obtain two recursive formulas for the power moments of
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Uncovering spatial representations from spatiotemporal patterns of rodent hippocampal field potentials. [PDF]
Cell Rep Methods, 2021 Cao L, Varga V, Chen ZS.
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Awake Hippocampal-Cortical Co-reactivation Is Associated with Forgetting. [PDF]
J Cogn Neurosci, 2023 Tanrıverdi B +6 more
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On the fourth power mean of the analogous general Kloosterman sum
Journal of Number Theory, 2016 The authors study generalized Kloosterman sums \[ C(m,n,k,\chi;q)= \sum_{a=1}^{q}\chi(a)e\left(\frac{m\bar a^k+na}{q }\right), \] where \(q\), \(m\), \(n\), \(k\) are given positive integers, \(q \geq 3\), \(e(x)=e^{2\pi i x}\), \(a\bar a\equiv 1\pmod{q}\) and \(\chi\) is a character \(\mod{q}\).
Chen, Hui, Zhang, Tianping
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A note on the fourth power mean of the generalized Kloosterman sums
Journal of Number Theory, 2017 Let \(p\) be an odd prime, and let \(\alpha\geq 2\) be an integer. Let \(\chi\) be any non-primitive character modulo \(p^{\alpha}\) satisfying \(\chi\neq \chi_0\), the principal character. Let \(n\) be an integer with \((n, p)=1\). This paper proves that \[ \mathop{\sum_{m=1}^{p^{\alpha}}}_{(m,p)=1}\left|\sum_{a=1}^{p^{\alpha}}\chi(a)e\left(\frac{ma+n\
Zhang, Wenpeng, Shen, Shimeng
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On the Hybrid Mean Value of Generalized Dedekind Sums, Generalized Hardy Sums and Kloosterman Sums
, 2018 The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums, and give some exact computational formulae for them by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function.
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