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1

., Editores. "Elenor Kunz." Motrivivência 27, no. 44 (2015): 219. http://dx.doi.org/10.5007/38538.

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2

Gottschalk, J. "Jochen Kunz." Der Pathologe 37, S2 (2016): 263–64. http://dx.doi.org/10.1007/s00292-016-0201-9.

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3

Trivedi, V. "Hilbert-Kunz density function and Hilbert-Kunz multiplicity." Transactions of the American Mathematical Society 370, no. 12 (2018): 8403–28. http://dx.doi.org/10.1090/tran/7268.

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4

Richardson, Christopher S., Wendy Hood, Louise Allen, et al. "Thomas H. Kunz." Physiological and Biochemical Zoology 94, no. 4 (2021): 253–67. http://dx.doi.org/10.1086/714937.

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5

Watanabe, Kei-Ichi, and Ken-Ichi Yoshida. "Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings." Nagoya Mathematical Journal 162 (June 2001): 87–110. http://dx.doi.org/10.1017/s0027763000007819.

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We study the behavior of Hilbert-Kunz multiplicity for powers of an ideal, especially the case of stable ideals and ideals in local rings of dimension 2. We can characterize regular local rings by certain equality between Hilbert-Kunz multiplicity and usual multiplicity.We show that rings with “minimal” Hilbert-Kunz multiplicity relative to usual multiplicity are “Veronese subrings” in dimension 2.
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6

Trivedi, V. "Asymptotic Hilbert–Kunz multiplicity." Journal of Algebra 492 (December 2017): 498–523. http://dx.doi.org/10.1016/j.jalgebra.2017.09.019.

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7

Niemeier, Hans-Martin. "Martin Kunz Memorial Lecture." Journal of Air Transport Management 11, no. 1 (2005): 1–2. http://dx.doi.org/10.1016/j.jairtraman.2004.11.002.

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8

Künzel, Rudi. "Tijd in de historische sociologie van Ibn Khaldûn." Tijdschrift voor geschiedenis 132, no. 2 (2019): 159–80. http://dx.doi.org/10.5117/tvgesch2019.2.002.kunz.

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9

Aberbach, Ian M., and Florian Enescu. "New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension." Nagoya Mathematical Journal 212 (December 2013): 59–85. http://dx.doi.org/10.1017/s0027763000022376.

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AbstractWe present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.
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10

Aberbach, Ian M., and Florian Enescu. "New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension." Nagoya Mathematical Journal 212 (December 2013): 59–85. http://dx.doi.org/10.1215/00277630-2335204.

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AbstractWe present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.
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11

Upadhyay, Shyamashree. "The Hilbert-Kunz Function for Binomial Hypersurfaces." Algebra 2014 (November 27, 2014): 1–15. http://dx.doi.org/10.1155/2014/525467.

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I give an iterative closed form formula for the Hilbert-Kunz function for any binomial hypersurface in general, over any field of arbitrary positive characteristic. I prove that the Hilbert-Kunz multiplicity associated with any binomial hypersurface over any field of arbitrary positive characteristic is rational. As an example, I also prove the well known fact that for 1-dimensional binomial hypersurfaces the Hilbert-Kunz multiplicity is a positive integer and give a precise account of the integer.
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12

Mondal, Mandira, and V. Trivedi. "Hilbert–Kunz density function and asymptotic Hilbert–Kunz multiplicity for projective toric varieties." Journal of Algebra 520 (February 2019): 479–516. http://dx.doi.org/10.1016/j.jalgebra.2018.10.038.

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13

Stöhr, Dominique. "Kunz, Hans-Martin: Mahasweta Devi." Anthropos 102, no. 2 (2007): 635–36. http://dx.doi.org/10.5771/0257-9774-2007-2-635.

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14

Fenton, M. Brock, and Sharon Swartz. "Thomas H. Kunz (1938–2020)." Nature Ecology & Evolution 4, no. 8 (2020): 1002–3. http://dx.doi.org/10.1038/s41559-020-1224-4.

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15

Malatova, I., J. Hulka, and E. Goldfinch. "Emil Kunz (+25 January 2012)." Radiation Protection Dosimetry 149, no. 4 (2012): 355–56. http://dx.doi.org/10.1093/rpd/ncs046.

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16

Watanabe, Kei-ichi, and Ken-ichi Yoshida. "Minimal relative Hilbert-Kunz multiplicity." Illinois Journal of Mathematics 48, no. 1 (2004): 273–94. http://dx.doi.org/10.1215/ijm/1258136184.

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17

Smirnov, Ilya. "Equimultiplicity in Hilbert–Kunz theory." Mathematische Zeitschrift 291, no. 1-2 (2018): 245–78. http://dx.doi.org/10.1007/s00209-018-2082-5.

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18

Alhajjar, Elie, Travis Russell, and Michael Steward. "Numerical semigroups and Kunz polytopes." Semigroup Forum 99, no. 1 (2019): 153–68. http://dx.doi.org/10.1007/s00233-019-10028-x.

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19

TRIVEDI, V. "Nonfiniteness of Hilbert–Kunz functions." Proceedings - Mathematical Sciences 127, no. 2 (2017): 263–68. http://dx.doi.org/10.1007/s12044-017-0329-4.

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20

Han, C., and P. Monsky. "Some surprising Hilbert-Kunz functions." Mathematische Zeitschrift 214, no. 1 (1993): 119–35. http://dx.doi.org/10.1007/bf02572395.

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21

Perez, Mar. "In Tribute to Stefan Kunz." Viruses 13, no. 9 (2021): 1840. http://dx.doi.org/10.3390/v13091840.

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22

Pascual, Manuel. "Tribute to Professor Stefan Kunz." Viruses 13, no. 9 (2021): 1862. http://dx.doi.org/10.3390/v13091862.

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23

Goel, Kriti, Mitra Koley, and J. K. Verma. "Hilbert-Kunz function and Hilbert-Kunz multiplicity of some ideals of the Rees algebra." Communications in Algebra 49, no. 7 (2021): 3066–84. http://dx.doi.org/10.1080/00927872.2021.1887881.

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24

BRENNER, HOLGER, and ALESSIO CAMINATA. "GENERALIZED HILBERT–KUNZ FUNCTION IN GRADED DIMENSION 2." Nagoya Mathematical Journal 230 (December 5, 2016): 1–17. http://dx.doi.org/10.1017/nmj.2016.66.

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We prove that the generalized Hilbert–Kunz function of a graded module $M$ over a two-dimensional standard graded normal $K$-domain over an algebraically closed field $K$ of prime characteristic $p$ has the form $gHK(M,q)=e_{gHK}(M)q^{2}+\unicode[STIX]{x1D6FE}(q)$, with rational generalized Hilbert–Kunz multiplicity $e_{gHK}(M)$ and a bounded function $\unicode[STIX]{x1D6FE}(q)$. Moreover, we prove that if $R$ is a $\mathbb{Z}$-algebra, the limit for $p\rightarrow +\infty$ of the generalized Hilbert–Kunz multiplicity $e_{gHK}^{R_{p}}(M_{p})$ over the fibers $R_{p}$ exists, and it is a rational number.
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25

Galassi, Diana M. P. "The genus Pseudectinosoma KUNZ, 1935: an update, and description of Pseudectinosoma kunzi sp. n. from Italy (Crustacea: Copepoda: Ectinosomatidae)." Archiv für Hydrobiologie 139, no. 2 (1997): 277–87. http://dx.doi.org/10.1127/archiv-hydrobiol/139/1997/277.

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26

wha. "DPB-Geschäftsführer Hans-Detlev Kunz verabschiedet." Der Deutsche Dermatologe 66, no. 11 (2018): 804. http://dx.doi.org/10.1007/s15011-018-2169-7.

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27

Celikbas, Olgur, Hailong Dao, Craig Huneke, and Yi Zhang. "Bounds on the Hilbert-Kunz multiplicity." Nagoya Mathematical Journal 205 (March 2012): 149–65. http://dx.doi.org/10.1017/s0027763000010473.

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AbstractIn this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed nonregular local rings, bounding them uniformly away from 1. Our results improve previous work of Aberbach and Enescu.
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28

Opatz, Till. "A tribute to Professor Horst Kunz." Arkivoc 2021, no. 4 (2020): 1–17. http://dx.doi.org/10.24820/ark.5550190.p001.481.

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29

Heinz, Franz X. "Obituary for Christian Kunz, 1927–2020." Ticks and Tick-borne Diseases 11, no. 4 (2020): 101474. http://dx.doi.org/10.1016/j.ttbdis.2020.101474.

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30

Hanes, Douglas. "Notes on the Hilbert–Kunz function." Journal of Algebra 265, no. 2 (2003): 619–30. http://dx.doi.org/10.1016/s0021-8693(03)00233-3.

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31

Celikbas, Olgur, Hailong Dao, Craig Huneke, and Yi Zhang. "Bounds on the Hilbert-Kunz multiplicity." Nagoya Mathematical Journal 205 (March 2012): 149–65. http://dx.doi.org/10.1215/00277630-1543805.

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AbstractIn this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed nonregular local rings, bounding them uniformly away from 1. Our results improve previous work of Aberbach and Enescu.
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32

Huneke, Craig, Moira A. McDermott, and Paul Monsky. "Hilbert-Kunz Functions for Normal Rings." Mathematical Research Letters 11, no. 4 (2004): 539–46. http://dx.doi.org/10.4310/mrl.2004.v11.n4.a11.

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33

Núñez-Betancourt, Luis, and Ilya Smirnov. "Hilbert–Kunz multiplicities and F-thresholds." Boletín de la Sociedad Matemática Mexicana 26, no. 1 (2018): 15–25. http://dx.doi.org/10.1007/s40590-018-0226-6.

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34

Chang, Shou-Te. "Hilbert-Kunz functions and Frobenius functors." Transactions of the American Mathematical Society 349, no. 3 (1997): 1091–119. http://dx.doi.org/10.1090/s0002-9947-97-01704-2.

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35

Heinz, Franz X. "Obituary for Christian Kunz, 1927–2020." Wiener klinische Wochenschrift 132, no. 13-14 (2020): 410–11. http://dx.doi.org/10.1007/s00508-020-01680-3.

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36

Grundguth, Reinhold. "Die Kunz GmbH verbessert ihr Rating." Bankfachklasse 28, no. 9 (2006): 4–15. http://dx.doi.org/10.1007/bf03255257.

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37

Epstein, Neil, and Yongwei Yao. "Some extensions of Hilbert–Kunz multiplicity." Collectanea Mathematica 68, no. 1 (2016): 69–85. http://dx.doi.org/10.1007/s13348-016-0174-2.

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38

Krost, Heidrun. "Haka Kunz setzt auf stationäres Geschäft." Lebensmittel Zeitung 73, no. 31 (2021): 12. http://dx.doi.org/10.51202/0947-7527-2021-31-012.

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39

Kunz, Karen. "Postmodern Public Administration." Public Voices 10, no. 1 (2016): 104. http://dx.doi.org/10.22140/pv.140.

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40

Almeida, Andrea Silvânia de, and Bianca Bissoli Lucas. "A educação física sob direção de Kunz." Conexões 8, no. 1 (2010): 77–99. http://dx.doi.org/10.20396/conex.v8i1.8637756.

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Este ensaio explora uma síntese do pensamento do professor Elenor Kunz, com o propósito vital de tornar compreensível à forma de pensar a educação física, especialmente, escolar e, não exaltá-lo enquanto uma pessoa ímpar que propôs uma abordagem verdadeiramente absoluta para a educação física brasileira. Sua abordagem nos permite compreender o fazer pedagógico considerando o indivíduo em seus aspectos biológico, político, social e psíquico. Assim como, vem convidar ao leitor para incomodar-se com sua prática e buscar aprofundar-se nas bases epistemológicas que dão sustentação a teoria, já que aqui é uma exploração sucinta.
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41

Trivedi, V. "Hilbert-Kunz Multiplicity and Reduction Mod p." Nagoya Mathematical Journal 185 (2007): 123–41. http://dx.doi.org/10.1017/s0027763000025770.

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AbstractWe show that the Hilbert-Kunz multiplicities of the reductions to positive characteristics of an irreducible projective curve in characteristic 0 have a well-defined limit as the characteristic tends to infinity.
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42

Epstein, Neil, and Javid Validashti. "Hilbert-Kunz multiplicity of products of ideals." Journal of Commutative Algebra 11, no. 2 (2019): 225–36. http://dx.doi.org/10.1216/jca-2019-11-2-225.

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43

Vraciu, Adela. "An observation on generalized Hilbert-Kunz functions." Proceedings of the American Mathematical Society 144, no. 8 (2016): 3221–29. http://dx.doi.org/10.1090/proc/13000.

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44

Blickle, Manuel, and Florian Enescu. "On rings with small Hilbert-Kunz multiplicity." Proceedings of the American Mathematical Society 132, no. 9 (2004): 2505–9. http://dx.doi.org/10.1090/s0002-9939-04-07469-6.

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45

Trivedi, Vijaylaxmi, and Kei-Ichi Watanabe. "Hilbert-Kunz density functions and F-thresholds." Journal of Algebra 567 (February 2021): 533–63. http://dx.doi.org/10.1016/j.jalgebra.2020.09.025.

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46

Trivedi, V. "Hilbert–Kunz functions of a Hirzebruch surface." Journal of Algebra 457 (July 2016): 405–30. http://dx.doi.org/10.1016/j.jalgebra.2016.02.026.

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47

Trivedi, V. "Semistability and Hilbert–Kunz multiplicities for curves." Journal of Algebra 284, no. 2 (2005): 627–44. http://dx.doi.org/10.1016/j.jalgebra.2004.10.016.

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48

Monsky, Paul. "Hilbert–Kunz functions for irreducible plane curves." Journal of Algebra 316, no. 1 (2007): 326–45. http://dx.doi.org/10.1016/j.jalgebra.2007.03.028.

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49

Chiang, Li, and Yu-Ching Hung. "On Hilbert–Kunz Functions of Some Hypersurfaces." Journal of Algebra 199, no. 2 (1998): 499–527. http://dx.doi.org/10.1006/jabr.1997.7206.

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50

Smith, Larry. "Hilbert–Kunz invariants and Euler characteristic polynomials." Pacific Journal of Mathematics 262, no. 1 (2013): 227–55. http://dx.doi.org/10.2140/pjm.2013.262.227.

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