# Mean square value of exponential sums related to representation of integers as sum of two squares

Pavel M. Bleher; Freeman J. Dyson

Acta Arithmetica (1994)

- Volume: 68, Issue: 1, page 71-84
- ISSN: 0065-1036

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topPavel M. Bleher, and Freeman J. Dyson. "Mean square value of exponential sums related to representation of integers as sum of two squares." Acta Arithmetica 68.1 (1994): 71-84. <http://eudml.org/doc/206644>.

@article{PavelM1994,

author = {Pavel M. Bleher, Freeman J. Dyson},

journal = {Acta Arithmetica},

keywords = {exponential sums; representation of integers as sum of two squares; error function in the shifted circle problem; limit distribution; mean square value},

language = {eng},

number = {1},

pages = {71-84},

title = {Mean square value of exponential sums related to representation of integers as sum of two squares},

url = {http://eudml.org/doc/206644},

volume = {68},

year = {1994},

}

TY - JOUR

AU - Pavel M. Bleher

AU - Freeman J. Dyson

TI - Mean square value of exponential sums related to representation of integers as sum of two squares

JO - Acta Arithmetica

PY - 1994

VL - 68

IS - 1

SP - 71

EP - 84

LA - eng

KW - exponential sums; representation of integers as sum of two squares; error function in the shifted circle problem; limit distribution; mean square value

UR - http://eudml.org/doc/206644

ER -

## References

top- [B] P. M. Bleher, On the distribution of the number of lattice points inside a family of convex ovals, Duke Math. J. 67 (1992), 461-481. Zbl0762.11031
- i[BCDL] P. M. Bleher, Z. Cheng, F. J. Dyson and J. L. Lebowitz, Distribution of the error term for the number of lattice points inside a shifted circle, Comm. Math. Phys. 154 (1993), 433-469. Zbl0781.11038
- [BD] P. M. Bleher and F. J. Dyson, The variance of the error function in the shifted circle problem is a wild function of the shift, Comm. Math. Phys., to appear. Zbl0808.11058
- [C] H. Cramér, Über zwei Sätze von Herrn G. H. Hardy, Math. Z. 15 (1922), 201-210.
- [H] G. H. Hardy, The average order of the arithmetic functions P(x) and Δ(x), Proc. London Math. Soc. 15 (1916), 192-213. Zbl46.0262.01
- [HL] G. H. Hardy and J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet series whose coefficients are positive, Proc. London Math. Soc. 13 (1914), 174. Zbl45.0389.02
- [HW] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford, 1960.
- [H-B] D. R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, Acta Arith. 60 (1992), 389-415. Zbl0725.11045

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