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Journal articles on the topic 'Exponential sums'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 February 2023

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1

Shparlinski, Igor E., and José Felipe Voloch. "Binomial exponential sums." ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE 21, no. 2 (December 2020): 931–41. http://dx.doi.org/10.2422/2036-2145.201811_007.

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2

Krätzel, Ekkehard. "DOUBLE EXPONENTIAL SUMS." Analysis 16, no. 2 (June 1996): 109–24. http://dx.doi.org/10.1524/anly.1996.16.2.109.

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3

Kerr, B. "INCOMPLETE EXPONENTIAL SUMS OVER EXPONENTIAL FUNCTIONS." Quarterly Journal of Mathematics 66, no. 1 (June 16, 2014): 213–24. http://dx.doi.org/10.1093/qmath/hau015.

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4

Shparlinski, Igor E., and Kam Hung Yau. "Double exponential sums with exponential functions." International Journal of Number Theory 13, no. 10 (October 16, 2017): 2531–43. http://dx.doi.org/10.1142/s179304211750141x.

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We obtain several estimates for double rational exponential sums modulo a prime [Formula: see text] with products [Formula: see text] where both [Formula: see text] and [Formula: see text] run through short intervals and [Formula: see text] is fixed integer. We also obtain some new estimates for the number of points on exponential modular curves [Formula: see text] and similar.
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5

Proskurin, N. V. "On Cubic Exponential Sums and Gauss Sums." Journal of Mathematical Sciences 234, no. 5 (September 10, 2018): 697–700. http://dx.doi.org/10.1007/s10958-018-4037-0.

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6

Cochrane, Todd, Christopher Pinner, and Jason Rosenhouse. "Sparse polynomial exponential sums." Acta Arithmetica 108, no. 1 (2003): 37–52. http://dx.doi.org/10.4064/aa108-1-4.

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7

Štefaňák, M., D. Haase, W. Merkel, M. S. Zubairy, and W. P. Schleich. "Factorization with exponential sums." Journal of Physics A: Mathematical and Theoretical 41, no. 30 (July 15, 2008): 304024. http://dx.doi.org/10.1088/1751-8113/41/30/304024.

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8

Erdélyi, T. "Inequalities for exponential sums." Sbornik: Mathematics 208, no. 3 (March 31, 2017): 433–64. http://dx.doi.org/10.1070/sm8670.

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9

Fouvry, Etienne, and Henryk Iwaniec. "Exponential sums with monomials." Journal of Number Theory 33, no. 3 (November 1989): 311–33. http://dx.doi.org/10.1016/0022-314x(89)90067-x.

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10

Adolphson, Alan, and Steven Sperber. "On twisted exponential sums." Mathematische Annalen 290, no. 1 (March 1991): 713–26. http://dx.doi.org/10.1007/bf01459269.

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11

Jun, Byungheup, and Jungyun Lee. "Equidistribution of generalized Dedekind sums and exponential sums." Journal of Number Theory 137 (April 2014): 67–92. http://dx.doi.org/10.1016/j.jnt.2013.10.020.

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12

Zaharescu, Alexandru. "Averages of short exponential sums." Acta Arithmetica 88, no. 3 (1999): 223–31. http://dx.doi.org/10.4064/aa-88-3-223-231.

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13

Cochrane, Todd, and Zhiyong Zheng. "Pure and mixed exponential sums." Acta Arithmetica 91, no. 3 (1999): 249–78. http://dx.doi.org/10.4064/aa-91-3-249-278.

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14

Cao, Xiaodong, and Wenguang Zhai. "Multiple exponential sums with monomials." Acta Arithmetica 92, no. 3 (2000): 195–213. http://dx.doi.org/10.4064/aa-92-3-195-213.

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15

Cochrane, Todd. "Exponential sums modulo prime powers." Acta Arithmetica 101, no. 2 (2002): 131–49. http://dx.doi.org/10.4064/aa101-2-5.

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16

Li, Peigen. "Exponential sums and rigid cohomology." Finite Fields and Their Applications 81 (August 2022): 102031. http://dx.doi.org/10.1016/j.ffa.2022.102031.

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17

Wan, Daqing. "Exponential Sums over Finite Fields." Journal of Systems Science and Complexity 34, no. 4 (August 2021): 1225–78. http://dx.doi.org/10.1007/s11424-021-0066-8.

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18

Shparlinski, Igor E. "Exponential Sums with Farey Fractions." Bulletin of the Polish Academy of Sciences Mathematics 57, no. 2 (2009): 101–7. http://dx.doi.org/10.4064/ba57-2-2.

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19

Birch, Bryan J., and Enrico Bombieri. "Appendix: On Some Exponential Sums." Annals of Mathematics 121, no. 2 (March 1985): 345. http://dx.doi.org/10.2307/1971176.

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20

Adolphson, Alan, and Steven Sperber. "Exponential sums and Newton polyhedra." Bulletin of the American Mathematical Society 16, no. 2 (April 1, 1987): 282–87. http://dx.doi.org/10.1090/s0273-0979-1987-15518-2.

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21

Huxley, M. N. "Exponential Sums and Rounding Error." Journal of the London Mathematical Society s2-43, no. 2 (April 1991): 367–84. http://dx.doi.org/10.1112/jlms/s2-43.2.367.

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22

Loxton, J. H. "The distribution of exponential sums." Mathematika 32, no. 1 (June 1985): 16–25. http://dx.doi.org/10.1112/s0025579300010809.

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23

Friedlander, John B., Jan Hansen, and Igor E. Shparlinski. "Character sums with exponential functions." Mathematika 47, no. 1-2 (December 2000): 75–85. http://dx.doi.org/10.1112/s0025579300015734.

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24

Shparlinski, Igor E. "Bilinear sums with exponential functions." Proceedings of the American Mathematical Society 137, no. 07 (March 4, 2009): 2217–24. http://dx.doi.org/10.1090/s0002-9939-09-09882-7.

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25

Drappeau, Sary, and Clemens Müllner. "Exponential sums with automatic sequences." Acta Arithmetica 185, no. 1 (2018): 81–99. http://dx.doi.org/10.4064/aa171002-20-3.

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26

Huxley, M. N. "Exponential Sums and Lattice Points." Proceedings of the London Mathematical Society s3-60, no. 3 (May 1990): 471–502. http://dx.doi.org/10.1112/plms/s3-60.3.471.

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27

Health-Brown, D. R., and M. N. Huxley. "Exponential Sums with a Difference." Proceedings of the London Mathematical Society s3-61, no. 2 (September 1990): 227–50. http://dx.doi.org/10.1112/plms/s3-61.2.227.

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28

Huxley, M. N. "Exponential Sums and Lattice Points." Proceedings of the London Mathematical Society s3-66, no. 1 (January 1993): 70. http://dx.doi.org/10.1112/plms/s3-66.1.70-s.

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29

Banks, William D., Alessandro Conflitti, John B. Friedlander, and Igor E. Shparlinski. "Exponential sums over Mersenne numbers." Compositio Mathematica 140, no. 01 (January 2004): 15–30. http://dx.doi.org/10.1112/s0010437x03000022.

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30

Voloch, José Felipe, and Judy L. Walker. "Homogeneous weights and exponential sums." Finite Fields and Their Applications 9, no. 3 (July 2003): 310–21. http://dx.doi.org/10.1016/s1071-5797(03)00007-8.

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31

Bachman, Gennady. "Exponential sums with multiplicative coefficients." Electronic Research Announcements of the American Mathematical Society 5, no. 18 (October 29, 1999): 128–35. http://dx.doi.org/10.1090/s1079-6762-99-00071-2.

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32

Steinerberger, Stefan. "Exponential sums and Riesz energies." Journal of Number Theory 182 (January 2018): 37–56. http://dx.doi.org/10.1016/j.jnt.2017.08.002.

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33

Sergeyev, Yaroslav D. "Generation of symmetric exponential sums." Journal of Number Theory 108, no. 1 (September 2004): 60–75. http://dx.doi.org/10.1016/j.jnt.2004.04.010.

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34

Horbowicz, J., and H. Niederreiter. "Weighted exponential sums and discrepancy." Acta Mathematica Hungarica 54, no. 1-2 (March 1989): 89–97. http://dx.doi.org/10.1007/bf01950713.

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35

Indlekofer, K. H., and I. Kátai. "Exponential sums with multiplicative coefficients." Acta Mathematica Hungarica 54, no. 3-4 (September 1989): 263–68. http://dx.doi.org/10.1007/bf01952056.

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36

Gomez-Perez, Domingo, Jaime Gutierrez, and Igor E. Shparlinski. "Exponential sums with Dickson polynomials." Finite Fields and Their Applications 12, no. 1 (January 2006): 16–25. http://dx.doi.org/10.1016/j.ffa.2004.08.001.

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37

Danchenko, V. I., and A. E. Dodonov. "Estimates for exponential sums. Applications." Journal of Mathematical Sciences 188, no. 3 (December 15, 2012): 197–206. http://dx.doi.org/10.1007/s10958-012-1118-3.

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38

Adolphson, Alan, and Steven Sperber. "Exponential sums on A n." Israel Journal of Mathematics 120, no. 1 (December 2000): 3–21. http://dx.doi.org/10.1007/s11856-000-1269-7.

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39

Bourgain, J. "Estimates on polynomial exponential sums." Israel Journal of Mathematics 176, no. 1 (March 2010): 221–40. http://dx.doi.org/10.1007/s11856-010-0027-8.

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40

Cochrane, Todd, and Zhiyong Zheng. "Bounds for certain exponential sums." Asian Journal of Mathematics 4, no. 4 (2000): 757–74. http://dx.doi.org/10.4310/ajm.2000.v4.n4.a3.

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41

ADOLPHSON, ALAN, and STEVEN SPERBER. "EXPONENTIAL SUMS ON 𝔸n. IV." International Journal of Number Theory 05, no. 05 (August 2009): 747–64. http://dx.doi.org/10.1142/s1793042109002353.

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We find new conditions on a polynomial over a finite field that guarantee that the exponential sum defined by the polynomial has only one nonvanishing p-adic cohomology group, hence the L-function associated to the exponential sum is a polynomial or the reciprocal of a polynomial.
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42

Sun, Qingfeng, and Yuanying Wu. "Exponential sums involving Maass forms." Frontiers of Mathematics in China 9, no. 6 (February 19, 2014): 1349–66. http://dx.doi.org/10.1007/s11464-014-0360-z.

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43

Ergür, Alperen A., Grigoris Paouris, and J. Maurice Rojas. "Tropical varieties for exponential sums." Mathematische Annalen 377, no. 3-4 (January 31, 2019): 863–82. http://dx.doi.org/10.1007/s00208-019-01808-5.

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44

Fu, Lei. "Weights of twisted exponential sums." Mathematische Zeitschrift 262, no. 2 (June 28, 2008): 449–72. http://dx.doi.org/10.1007/s00209-008-0386-6.

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45

García López, Ricardo. "Exponential sums and singular hypersurfaces." manuscripta mathematica 97, no. 1 (August 1, 1998): 45–58. http://dx.doi.org/10.1007/s002290050084.

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46

Beylkin, Gregory, and Lucas Monzón. "Approximation by exponential sums revisited." Applied and Computational Harmonic Analysis 28, no. 2 (March 2010): 131–49. http://dx.doi.org/10.1016/j.acha.2009.08.011.

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47

Katz, N. M. "A Note on Exponential Sums." Finite Fields and Their Applications 1, no. 3 (July 1995): 395–98. http://dx.doi.org/10.1006/ffta.1995.1029.

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48

Han, Di, and Tingting Wang. "On the Dedekind sums and two-term exponential sums." Chinese Annals of Mathematics, Series B 36, no. 4 (June 27, 2015): 603–12. http://dx.doi.org/10.1007/s11401-015-0909-5.

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49

Shparlinski, Igor E. "On some exponential sums with exponential and rational functions." Rocky Mountain Journal of Mathematics 43, no. 1 (February 2013): 361–71. http://dx.doi.org/10.1216/rmj-2013-43-1-361.

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50

Li, Jianghua, and Tingting Wang. "A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums." Scientific World Journal 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/914591.

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The main purpose of this paper is using the analytic method, A. Weil’s classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it.
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