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Average number of lattice points in a disk
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2. | Mathematics Department, Malott Hall, Cornell Univeristy, Ithaca, NY 14853, United States |
References:
[1] |
M. Begué, T. Kalloniatis and R. Strichartz, Harmonic functions and the spectrum of the Laplacian on the Sierpinski carpet,, \emph{Fractals}, 21 (2013).
doi: 10.1142/S0218348X13500023. |
[2] |
P. Bleher, On the distribution of the number of lattice points inside a family of convex ovals,, \emph{Duke Math J.}, (): 461.
doi: 10.1215/S0012-7094-92-06718-4. |
[3] |
P. Bleher, Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems,, \emph{Duke Math J.}, (): 655.
doi: 10.1215/S0012-7094-93-07015-9. |
[4] |
M. Huxley, The mean lattice discrepancy,, \emph{Proc. Edinburg Math. Soc.}, 38 (1995), 523.
doi: 10.1017/S0013091500019313. |
[5] |
H. Iwaniec and E. Kowalski, Analytic Number Theory,, AMS Colloq. Publ. vol 53, (2004).
|
[6] |
S. Jayakar and R. Strichartz, Average number of lattice points in a disk,, \url{http://www.math.cornell.edu/ sujay/lattice}, (2012). Google Scholar |
[7] |
N. Lebedev, Special Functions and Their Applications,, Dover Publications, (1965).
|
[8] |
W. Müller, On the average order of the lattice rest of a convex body,, \emph{Acta Arith.}, 80 (1997), 89.
|
[9] |
C. Sogge, Hangzhou Lectures on Eigenfunctions of the Laplacian,, Princeton Univ. Press, (2014).
doi: 10.1515/9781400850549. |
[10] |
E. Stein and R. Shakarchi, Functional Analysis,, Princeton Univ. Press, (2011).
|
[11] |
R. Strichartz, Average error for spectral asymptotics on surfaces,, \emph{Comm. Pure Appl. Analysis}, 15 (2016), 9. Google Scholar |
show all references
References:
[1] |
M. Begué, T. Kalloniatis and R. Strichartz, Harmonic functions and the spectrum of the Laplacian on the Sierpinski carpet,, \emph{Fractals}, 21 (2013).
doi: 10.1142/S0218348X13500023. |
[2] |
P. Bleher, On the distribution of the number of lattice points inside a family of convex ovals,, \emph{Duke Math J.}, (): 461.
doi: 10.1215/S0012-7094-92-06718-4. |
[3] |
P. Bleher, Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems,, \emph{Duke Math J.}, (): 655.
doi: 10.1215/S0012-7094-93-07015-9. |
[4] |
M. Huxley, The mean lattice discrepancy,, \emph{Proc. Edinburg Math. Soc.}, 38 (1995), 523.
doi: 10.1017/S0013091500019313. |
[5] |
H. Iwaniec and E. Kowalski, Analytic Number Theory,, AMS Colloq. Publ. vol 53, (2004).
|
[6] |
S. Jayakar and R. Strichartz, Average number of lattice points in a disk,, \url{http://www.math.cornell.edu/ sujay/lattice}, (2012). Google Scholar |
[7] |
N. Lebedev, Special Functions and Their Applications,, Dover Publications, (1965).
|
[8] |
W. Müller, On the average order of the lattice rest of a convex body,, \emph{Acta Arith.}, 80 (1997), 89.
|
[9] |
C. Sogge, Hangzhou Lectures on Eigenfunctions of the Laplacian,, Princeton Univ. Press, (2014).
doi: 10.1515/9781400850549. |
[10] |
E. Stein and R. Shakarchi, Functional Analysis,, Princeton Univ. Press, (2011).
|
[11] |
R. Strichartz, Average error for spectral asymptotics on surfaces,, \emph{Comm. Pure Appl. Analysis}, 15 (2016), 9. Google Scholar |
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