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Journal articles on the topic 'Varieties of sums of powers'

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Author: Grafiati

Published: 14 March 2023

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1

Massarenti, Alex. "Generalized varieties of sums of powers." Bulletin of the Brazilian Mathematical Society, New Series 47, no. 3 (February 24, 2016): 911–34. http://dx.doi.org/10.1007/s00574-016-0196-0.

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2

Ranstad, K., and F. O. Schreyer. "Varieties of sums of power." Journal für die reine und angewandte Mathematik (Crelles Journal) 2000, no. 525 (August 11, 2000): 147–81. http://dx.doi.org/10.1515/crll.2000.064.

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3

Massarenti, Alex, and Massimiliano Mella. "Birational aspects of the geometry of Varieties of Sums of Powers." Advances in Mathematics 243 (August 2013): 187–202. http://dx.doi.org/10.1016/j.aim.2013.04.006.

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4

Iliev, Atanas, and Kristian Ranestad. "Canonical Curves and Varieties of Sums of Powers of Cubic Polynomials." Journal of Algebra 246, no. 1 (December 2001): 385–93. http://dx.doi.org/10.1006/jabr.2001.8942.

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5

Iliev, Atanas, and Kristian Ranestad. "$K3$ surfaces of genus 8 and varieties of sums of powers of cubic fourfolds." Transactions of the American Mathematical Society 353, no. 4 (October 11, 2000): 1455–68. http://dx.doi.org/10.1090/s0002-9947-00-02629-5.

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6

Bolognesi, Michele, and Alex Massarenti. "Varieties of sums of powers and moduli spaces of(1, 7)-polarized abelian surfaces." Journal of Geometry and Physics 125 (February 2018): 23–32. http://dx.doi.org/10.1016/j.geomphys.2017.12.004.

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7

Dolgachev, Igor V. "Dual Homogeneous Forms and Varieties of Power Sums." Milan Journal of Mathematics 72, no. 1 (October 2004): 163–87. http://dx.doi.org/10.1007/s00032-004-0029-2.

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8

Huang, Hang, Mateusz Michałek, and Emanuele Ventura. "Vanishing Hessian, wild forms and their border VSP." Mathematische Annalen 378, no. 3-4 (September 14, 2020): 1505–32. http://dx.doi.org/10.1007/s00208-020-02080-8.

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Abstract Wild forms are homogeneous polynomials whose smoothable rank is strictly larger than their border rank. The discrepancy between these two ranks is caused by the difference between the limit of spans of a family of zero-dimensional schemes and the span of their flat limit. For concise forms of minimal border rank, we show that the condition of vanishing Hessian is equivalent to being wild. This is proven by making a detour through structure tensors of smoothable and Gorenstein algebras. The equivalence fails in the non-minimal border rank regime. We exhibit an infinite series of minimal border rank wild forms of every degree $$d\ge 3$$ d ≥ 3 as well as an infinite series of wild cubics. Inspired by recent work on border apolarity of Buczyńska and Buczyński, we study the border varieties of sums of powers $$\underline{{\mathrm {VSP}}}$$ VSP ̲ of these forms in the corresponding multigraded Hilbert schemes.

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9

Heath-Brown, D. R. "Christopher Hooley. 7 August 1928—13 December 2018." Biographical Memoirs of Fellows of the Royal Society 69 (September 9, 2020): 225–46. http://dx.doi.org/10.1098/rsbm.2020.0027.

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Christopher Hooley was one of the leading analytic number theorists of his day, world-wide. His early work on Artin’s conjecture for primitive roots remains the definitive investigation in the area. His greatest contribution, however, was the introduction of exponential sums into every corner of analytic number theory, bringing the power of Deligne’s ‘Riemann hypothesis’ for varieties over finite fields to bear throughout the subject. For many he was a figure who bridged the classical period of Hardy and Littlewood with the modern era. This biographical sketch describes how he succeeded in applying the latest tools to famous old problems.

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10

Takagi, Hiromichi, and Francesco Zucconi. "Geometries of lines and conics on the quintic del Pezzo 3-fold and its application to varieties of power sums." Michigan Mathematical Journal 61, no. 1 (March 2012): 19–62. http://dx.doi.org/10.1307/mmj/1331222846.

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11

Evard, Jean-Claude, Hillel Gauchman, and Daniele Donini. "Sums of Powers and Powers of Sums: 10571." American Mathematical Monthly 105, no. 10 (December 1998): 959. http://dx.doi.org/10.2307/2589300.

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12

Tanton, James. "Sums of Powers." Math Horizons 11, no. 1 (September 2003): 15–20. http://dx.doi.org/10.1080/10724117.2003.12021732.

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13

Pollack, Paul, and Enrique Treviño. "Sums of Proper Powers." American Mathematical Monthly 128, no. 1 (January 2, 2021): 40. http://dx.doi.org/10.1080/00029890.2021.1847588.

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14

Conway, John B., Gabriel Prǎjiturǎ, and Alejandro Rodríguez-Martínez. "Powers and direct sums." Journal of Mathematical Analysis and Applications 413, no. 2 (May 2014): 880–89. http://dx.doi.org/10.1016/j.jmaa.2013.12.007.

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15

Jakimczuk, R. "Sums of perfect powers." International Journal of Contemporary Mathematical Sciences 8 (2013): 61–67. http://dx.doi.org/10.12988/ijcms.2013.13006.

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16

CHOI, H. TIMOTHY, and RONALD EVANS. "CONGRUENCES FOR SUMS OF POWERS OF KLOOSTERMAN SUMS." International Journal of Number Theory 03, no. 01 (March 2007): 105–17. http://dx.doi.org/10.1142/s1793042107000821.

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The nth power-moments Sn of classical Kloosterman sums (mod p) are known explicitly only for n ≤ 6. In 2002, we conjectured formulas for Sn (mod 4) for each n > 1, valid for all primes p > n. Here we prove these formulas, and give conjectural congruences for Sn modulo some higher powers of 2 for a few small values of n. For example, we conjecture that if p ≡ 17 (mod 120), so that p = 3s2 + 5t2, then [Formula: see text]

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17

Chrysafi, Loucas, and Carlos A. Marques. "Sums of Powers Via Matrices." Mathematics Magazine 94, no. 1 (January 1, 2021): 43–52. http://dx.doi.org/10.1080/0025570x.2021.1843889.

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18

Owens, Robert W. "Sums of Powers of Integers." Mathematics Magazine 65, no. 1 (February 1, 1992): 38. http://dx.doi.org/10.2307/2691359.

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19

Marik, Jan, and Clifford E. Weil. "Sums of Powers of Derivatives." Proceedings of the American Mathematical Society 112, no. 3 (July 1991): 807. http://dx.doi.org/10.2307/2048705.

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20

Moser, W. O. J. "75.30 Sums of dth Powers." Mathematical Gazette 75, no. 473 (October 1991): 332. http://dx.doi.org/10.2307/3619500.

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21

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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22

Eba, Hunde. "Sums of Powers of Integers." Missouri Journal of Mathematical Sciences 31, no. 1 (May 2019): 66–78. http://dx.doi.org/10.35834/mjms/1559181627.

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23

Beardon, A. F. "Sums of Powers of Integers." American Mathematical Monthly 103, no. 3 (March 1996): 201. http://dx.doi.org/10.2307/2975368.

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24

Mařík and Weil. "SUMS OF POWERS OF DERIVATIVES." Real Analysis Exchange 13, no. 1 (1987): 180. http://dx.doi.org/10.2307/44151867.

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25

Ryang, Dohyoung, and Tony Thompson. "Sums of Positive Integral Powers." Mathematics Teacher 106, no. 1 (August 2012): 71–77. http://dx.doi.org/10.5951/mathteacher.106.1.0071.

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26

Choudhry, Ajai. "Equal Sums of Like Powers." Rocky Mountain Journal of Mathematics 31, no. 1 (March 2001): 115–29. http://dx.doi.org/10.1216/rmjm/1008959671.

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27

Choudhry, Ajai. "Equal Sums of Seventh Powers." Rocky Mountain Journal of Mathematics 30, no. 3 (September 2000): 849–52. http://dx.doi.org/10.1216/rmjm/1021477247.

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28

Mař{í}k, Jan, and Clifford E. Weil. "Sums of powers of derivatives." Proceedings of the American Mathematical Society 112, no. 3 (March 1, 1991): 807. http://dx.doi.org/10.1090/s0002-9939-1991-1042268-1.

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29

Owens, Robert W. "Sums of Powers of Integers." Mathematics Magazine 65, no. 1 (February 1992): 38–40. http://dx.doi.org/10.1080/0025570x.1992.11995974.

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30

Cohen, S. "Sums of Two Exact Powers." Finite Fields and Their Applications 8, no. 4 (October 2002): 471–77. http://dx.doi.org/10.1016/s1071-5797(02)90354-0.

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31

Browning, T. D., and D. R. Heath-Brown. "Equal sums of three powers." Inventiones mathematicae 157, no. 3 (March 17, 2004): 553–73. http://dx.doi.org/10.1007/s00222-004-0360-9.

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32

Choudhry, Ajai. "On sums of eighth powers." Journal of Number Theory 39, no. 1 (September 1991): 104–7. http://dx.doi.org/10.1016/0022-314x(91)90037-c.

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33

Gao, Peng. "Sums of powers and majorization." Journal of Mathematical Analysis and Applications 340, no. 2 (April 2008): 1241–48. http://dx.doi.org/10.1016/j.jmaa.2007.09.058.

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34

Beardon, A. F. "Sums of Powers of Integers." American Mathematical Monthly 103, no. 3 (March 1996): 201–13. http://dx.doi.org/10.1080/00029890.1996.12004725.

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35

Páles, Zsolt. "Inequalities for sums of powers." Journal of Mathematical Analysis and Applications 131, no. 1 (April 1988): 265–70. http://dx.doi.org/10.1016/0022-247x(88)90204-1.

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36

Parks, Harold R. "Sums of non-integral powers." Journal of Mathematical Analysis and Applications 297, no. 1 (September 2004): 343–49. http://dx.doi.org/10.1016/j.jmaa.2004.05.001.

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37

Chen, Feng Juan. "Powers of general digital sums." Acta Mathematica Sinica, English Series 26, no. 6 (May 15, 2010): 1133–38. http://dx.doi.org/10.1007/s10114-010-8416-9.

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38

Gerard, Jane, and Lawrence C. Washington. "Sums of powers of primes." Ramanujan Journal 45, no. 1 (November 17, 2016): 171–80. http://dx.doi.org/10.1007/s11139-016-9847-4.

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39

Cohen, Stephen D., and Zhang Wenpeng. "Sums of Two Exact Powers." Finite Fields and Their Applications 8, no. 4 (October 2002): 471–77. http://dx.doi.org/10.1006/ffta.2002.0354.

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40

Choudhry, Ajai. "On Sums of Seventh Powers." Journal of Number Theory 81, no. 2 (April 2000): 266–69. http://dx.doi.org/10.1006/jnth.1999.2465.

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41

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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42

Popov, I. P. "Varieties of Mechanical Powers." Journal of Machinery Manufacture and Reliability 51, no. 8 (December 2022): 746–50. http://dx.doi.org/10.3103/s1052618822080155.

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43

Anglesio, Jean, and O. P. Lossers. "Periods from Sums of Powers: 10727." American Mathematical Monthly 108, no. 3 (March 2001): 273. http://dx.doi.org/10.2307/2695400.

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44

Boyadzhiev, Khristo N. "Sums of powers and special polynomials." Discussiones Mathematicae - General Algebra and Applications 40, no. 2 (2020): 275. http://dx.doi.org/10.7151/dmgaa.1336.

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45

Srdanov, Aleksa, and Nada Ratković Kovačević. "SUMS OF POWERS WITH Fk NUMBERS." JP Journal of Algebra, Number Theory and Applications 51, no. 1 (June 20, 2021): 77–95. http://dx.doi.org/10.17654/nt051010077.

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46

Wu, Dane W. "Bernoulli numbers and sums of powers." International Journal of Mathematical Education in Science and Technology 32, no. 3 (May 2001): 440–43. http://dx.doi.org/10.1080/00207390117519.

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47

Pigno, Vincent, and Christopher Pinner. "Binomial Character Sums Modulo Prime Powers." Journal de Théorie des Nombres de Bordeaux 28, no. 1 (2016): 39–53. http://dx.doi.org/10.5802/jtnb.927.

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48

Brüdern, Jörg. "Sums of Squares and Higher Powers." Journal of the London Mathematical Society s2-35, no. 2 (April 1987): 233–43. http://dx.doi.org/10.1112/jlms/s2-35.2.233.

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49

Choudhry, Ajai. "On Equal Sums of Sixth Powers." Rocky Mountain Journal of Mathematics 30, no. 3 (September 2000): 843–48. http://dx.doi.org/10.1216/rmjm/1021477246.

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50

Bremner, A., and Jean-Joël Delorme. "On equal sums of ninth powers." Mathematics of Computation 79, no. 269 (January 1, 2010): 603. http://dx.doi.org/10.1090/s0025-5718-09-02288-1.

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