Results 41 to 50 of about 803,219 (126)
Power-moments of SL$_3(\mathbb Z)$ Kloosterman sums
, 2013 summary:Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL$_2$ and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL$_3$
Djanković, Goran
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Distribution of integer points on determinant surfaces and a mod‐p analogue
Mathematika, Volume 72, Issue 2, April 2026.Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
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On Sums of hyper-Kloosterman Sums [PDF]
, 2022 A formula of Kuznetsov allows one to interpret a smooth sum of Kloosterman sums as a sum over the spectrum of $GL(2)$ automorphic forms. In this paper, we construct a similar formula for the first hyper-Kloosterman sums using $GL(3)$ automorphic forms ...
Buttcane, Jack
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Neurocognitive Dynamics of Translating Information From a Spatial Map Into Action
Psychophysiology, Volume 63, Issue 3, March 2026.ABSTRACT How do we translate information from a spatial map to action in our immediate surroundings? Despite the widespread use of various tools for orientation, from paper maps to GPS, this fundamental question remains unanswered in our understanding of human spatial navigation.
Maud Saulay‐Carret +3 more
wiley +1 more source
Experimental Physiology, Volume 111, Issue 3, Page 1210-1227, 1 March 2026.Abstract Historically, stroke and ageing have been associated with changes in narrow‐band periodic neuronal activity, but recent work has highlighted the importance of broad‐band aperiodic activity. Aperiodic activity is represented by the 1/f slope of power spectral density generated by cortical activity.
Asher J. Albertson +9 more
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INVERSION OF L-FUNCTIONS, GENERAL KLOOSTERMAN SUMS WEIGHTED BY INCOMPLETE CHARACTER SUMS [PDF]
Journal of the Korean Mathematical Society, 2010 The main purpose of this paper is using estimates for char- acter sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirich- let L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.
Xiaobeng Zhang, Huaning Liu
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An asymptotic local–global theorem on heights of some Kleinian group orbits
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We prove an asymptotic local–global theorem on the heights of point orbits of thin subgroups of Bianchi groups in H3$\mathbb {H}^3$.
Xuanxuan Xiao, Xin Zhang
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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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General Kloosterman sums over the ring of Gaussian integers [PDF]
Ukrainian Mathematical Journal, 2007 The general Kloosterman sum K(m, n; k; q) over ℤ was studied by S. Kanemitsu, Y. Tanigawa, Yuan Yi, and Wenpeng Zhang in their research of the problem of D. H. Lehmer. In the present paper, we obtain similar estimates for K(α, β; k; γ) over ℤ[i]. We also consider the sum \(\tilde K(\alpha ,\beta ;h,q;k)\), which does not have an analog in the ring ℤ ...
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A note on the mean value of the general Kloosterman sums [PDF]
, 2010 summary:The main purpose of this paper is to use the analytic method to study the calculating problem of the general Kloosterman sums, and give an exact calculating formula for ...
Yao, Weili, Liu, Huaning
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