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Journal articles on the topic 'Arith'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

Darkis, Debbie. "GCT Review: Arith-Magic II." Gifted Child Today Magazine 11, no. 4 (1988): 48. http://dx.doi.org/10.1177/107621758801100424.

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2

LING, DENGRONG, and MIN TANG. "SOME REMARKS ON MINIMAL ASYMPTOTIC BASES OF ORDER THREE." Bulletin of the Australian Mathematical Society 102, no. 1 (2020): 21–30. http://dx.doi.org/10.1017/s0004972719001345.

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3

BUDARINA, NATALIA. "ON A PROBLEM OF BERNIK, KLEINBOCK AND MARGULIS." Glasgow Mathematical Journal 53, no. 3 (2011): 669–81. http://dx.doi.org/10.1017/s0017089511000255.

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AbstractIn this paper, the Khintchine-type theorems of Beresnevich (Acta Arith.90(1999), 97) and Bernik (Acta Arith.53(1989), 17) for polynomials are generalised to incorporate a natural restriction on derivatives. This represents the first attempt to solve a problem posed by Bernik, Kleinbock and Margulis (Int. Math. Res. Notices2001(9) (2001), 453). More specifically, the main result provides a probabilistic criterion for the solvability of the system of inequalities |P(x)| < Ψ1(H) and |P′(x)| < Ψ2(H) in integral polynomialsPof degree ≤nand heightH, where Ψ1and Ψ2are fairly general err

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4

MEHER, JABAN. "SOME REMARKS ON RANKIN–COHEN BRACKETS OF EIGENFORMS." International Journal of Number Theory 08, no. 08 (2012): 2059–68. http://dx.doi.org/10.1142/s1793042112501175.

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We investigate the cases for which products of two quasimodular or nearly holomorphic eigenforms are eigenforms. We also generalize the results of Ghate [On products of eigenforms, Acta Arith.102 (2002) 27–44] to the case of Rankin–Cohen brackets.

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5

Liu, Huafeng, and Liqun Hu. "On the number of divisors of a quaternary quadratic form." International Journal of Number Theory 12, no. 05 (2016): 1219–35. http://dx.doi.org/10.1142/s1793042116500755.

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Let [Formula: see text] We obtain the asymptotic formula [Formula: see text] where [Formula: see text] are two constants. This improves the previous error term [Formula: see text] obtained by the second author [An asymptotic formula related to the divisors of the quaternary quadratic form, Acta Arith. 166 (2014) 129–140].

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6

DICKINSON, DETTA, and MUMTAZ HUSSAIN. "THE METRIC THEORY OF MIXED TYPE LINEAR FORMS." International Journal of Number Theory 09, no. 01 (2012): 77–90. http://dx.doi.org/10.1142/s1793042112501278.

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In this paper the metric theory of Diophantine approximation of linear forms that are of mixed type is investigated. Khintchine–Groshev theorems are established together with the Hausdorff measure generalizations. The latter includes the original dimension results obtained in [H. Dickinson, The Hausdorff dimension of sets arising in metric Diophantine approximation, Acta Arith.68(2) (1994) 133–140] as special cases.

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7

KERR, BRYCE. "SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS." Bulletin of the Australian Mathematical Society 88, no. 3 (2013): 435–47. http://dx.doi.org/10.1017/s0004972713000324.

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AbstractWe use a generalisation of Vinogradov’s mean value theorem of Parsell et al. [‘Near-optimal mean value estimates for multidimensional Weyl sums’, arXiv:1205.6331] and ideas of Schmidt [‘Irregularities of distribution. IX’, Acta Arith. 27 (1975), 385–396] to give nontrivial bounds for the number of solutions to polynomial congruences, when the solutions lie in a very general class of sets, including all convex sets.

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8

ZHU, HUILIN, MAOHUA LE, and ALAIN TOGBÉ. "ON THE EXPONENTIAL DIOPHANTINE EQUATION x2+p2m=2yn." Bulletin of the Australian Mathematical Society 86, no. 2 (2012): 303–14. http://dx.doi.org/10.1017/s000497271200010x.

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AbstractLet p be an odd prime. In this paper, we consider the equation and we describe all its solutions. Moreover, we prove that this equation has no solution (x,y,m,n) when n>3 is an odd prime and y is not the sum of two consecutive squares. This extends the work of Tengely [On the diophantine equation x2+q2m=2yp, Acta Arith.127(1) (2007), 71–86].

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9

Silva de Souza, C. H., and J. N. Tomazella. "Erratum to “Magic $p$-dimensional cubes” (Acta Arith. 96 (2001), 361–364)." Acta Arithmetica 191, no. 1 (2019): 95–100. http://dx.doi.org/10.4064/aa190409-9-7.

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10

Kühnlein, Stefan. "Erratum to ``Cohomology sets inside arithmetic groups'' (Acta Arith. 107 (2003), 27–33)." Acta Arithmetica 110, no. 2 (2003): 201. http://dx.doi.org/10.4064/aa110-2-9.

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11

Boutabaa, W., William Cherry, and Alain Escassut. "Erratum to ``Unique range sets in positive characteristic'' (Acta Arith. 103 (2002), 169–189)." Acta Arithmetica 105, no. 3 (2002): 303. http://dx.doi.org/10.4064/aa105-3-6.

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12

Helou, Charles. "Corrigendum to ``Norm residue symbol and cyclotomic units'' (Acta Arith. 73 (1995), 147–188)." Acta Arithmetica 98, no. 3 (2001): 311. http://dx.doi.org/10.4064/aa98-3-7.

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13

Kochanek, Tomasz. "Corrigendum to ``Stability aspects of arithmetic functions, II'' (Acta Arith. 139 (2009), 131–146)." Acta Arithmetica 149, no. 1 (2011): 83–98. http://dx.doi.org/10.4064/aa149-1-6.

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14

Cobbe, Alessandro. "A representative of RΓ(N,T) for higher dimensional twists of ℤpr(1)". International Journal of Number Theory 17, № 08 (2021): 1925–49. http://dx.doi.org/10.1142/s1793042121500706.

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Let [Formula: see text] be a Galois extension of [Formula: see text]-adic number fields and let [Formula: see text] be a de Rham representation of the absolute Galois group [Formula: see text] of [Formula: see text]. In the case [Formula: see text], the equivariant local [Formula: see text]-constant conjecture describes the compatibility of the equivariant Tamagawa number conjecture with the functional equation of Artin [Formula: see text]-functions and it can be formulated as the vanishing of a certain element [Formula: see text] in [Formula: see text]; a similar approach can be followed also

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15

Mehta, Jay, and G. K. Viswanadham. "Quasi-uniqueness of the set of "Gaussian prime plus one's"." International Journal of Number Theory 10, no. 07 (2014): 1783–90. http://dx.doi.org/10.1142/s1793042114500559.

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We recall the well-known notion of the set of uniqueness for arithmetical functions, introduced by Kátai and several other mathematicians like Indlekofer, Elliot and Hoffman, independently. We define its analogue for completely additive complex-valued functions over the set of non-zero Gaussian integers with some examples. We show that the set of "Gaussian prime plus one's" along with finitely many Gaussian primes of norm up to some constant K is a set of uniqueness with respect to Gaussian integers. This is analogous to Kátai's result in the case of positive integers [I. Kátai, On sets charac

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16

Kim, Sungjin. "On the order of a modulo n, on average." International Journal of Number Theory 12, no. 08 (2016): 2073–80. http://dx.doi.org/10.1142/s1793042116501244.

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Let [Formula: see text] be an integer. Denote by [Formula: see text] the multiplicative order of [Formula: see text] modulo integer [Formula: see text]. We prove that there is a positive constant [Formula: see text] such that if [Formula: see text], then [Formula: see text] where [Formula: see text] It was known for [Formula: see text] in [P. Kurlberg and C. Pomerance, On a problem of Arnold: The average multiplicative order of a given integer, Algebra Number Theory 7 (2013) 981–999] in which they refer to [F. Luca and I. E. Shparlinski, Average multiplicative orders of elements modulo [Formul

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17

Schinzel, A. "Corrigendum to the paper “Reducibility of lacunary polynomials XII” Acta Arith. 90 (1999), 273–289." Acta Arithmetica 188, no. 1 (2019): 99. http://dx.doi.org/10.4064/aa-90-3-273-289-c.

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18

Fried, M., and A. Schinzel. "Corrigendum and addendum to the paper ``Reducibility of quadrinomials" (Acta Arith. 21 (1972), 153–171)." Acta Arithmetica 99, no. 4 (2001): 409–10. http://dx.doi.org/10.4064/aa99-4-7.

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19

Cass, Stephen. "4-Bit wonder: Explore the guts of computing with arith-matic's S1-AU kit - [Resources]." IEEE Spectrum 55, no. 8 (2018): 14–15. http://dx.doi.org/10.1109/mspec.2018.8423574.

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20

DEKA BARUAH, NAYANDEEP, and KALLOL NATH. "INFINITE FAMILIES OF ARITHMETIC IDENTITIES FOR 4-CORES." Bulletin of the Australian Mathematical Society 87, no. 2 (2012): 304–15. http://dx.doi.org/10.1017/s0004972712000378.

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AbstractLetu(n) andv(n) be the number of representations of a nonnegative integernin the formsx2+4y2+4z2andx2+2y2+2z2, respectively, withx,y,z∈ℤ, and leta4(n) andr3(n) be the number of 4-cores ofnand the number of representations ofnas a sum of three squares, respectively. By employing simple theta-function identities of Ramanujan, we prove that$u(8n+5)=8a_4(n)=v(8n+5)=\frac {1}{3}r_3(8n+5)$. With the help of this and a classical result of Gauss, we find a simple proof of a result ona4(n) proved earlier by K. Ono and L. Sze [‘4-core partitions and class numbers’,Acta Arith.80(1997), 249–272].

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21

Girstmair, Kurt. "Corrigendum to the paper: ``Linear relations between roots of polynomials" (Acta Arith. 89 (1999), 53–96)." Acta Arithmetica 110, no. 2 (2003): 203. http://dx.doi.org/10.4064/aa110-2-10.

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22

Gurak, S. "Correction to ``Minimal polynomials for Gauss periods with f=2'' (Acta Arith. 121 (2006), 233–257)." Acta Arithmetica 132, no. 3 (2008): 299. http://dx.doi.org/10.4064/aa132-3-5.

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23

Kölle, Michael, and Peter Schmid. "Correction to ``Computing Galois groups by means of Newton polygons'' (Acta Arith. 115 (2004), 71–84)." Acta Arithmetica 140, no. 1 (2009): 101–3. http://dx.doi.org/10.4064/aa140-1-7.

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24

Bhowmik, Gautami, and Jan-Christoph Schlage-Puchta. "Corrigendum to ``An improvement on Olson's constant for Zp⨁Zp'' (Acta Arith. 141 (2010), 311–319)." Acta Arithmetica 149, no. 1 (2011): 99–100. http://dx.doi.org/10.4064/aa149-1-7.

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25

Tahay, Pierre-Adrien. "Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size." Uniform distribution theory 15, no. 1 (2020): 1–26. http://dx.doi.org/10.2478/udt-2020-0001.

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AbstractIn 2009, Grant, Shallit, and Stoll [Acta Arith. 140 (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2 in cases where the size of the alphabet is a prime number or a squarefree product of primes. We establish similar results for an even larger family of pseudorandom sequences, constructed via difference matrices, in the case of an alphabet of any size. The constructions generalize those from Grant et al. In the case

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26

Walsh, P. "Corrections to "A quantitative version of Runge's theorem on diophantine equations" (Acta Arith. 62 (1992), 157-172)." Acta Arithmetica 73, no. 4 (1995): 397–98. http://dx.doi.org/10.4064/aa-73-4-397-398.

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27

Bhowmik, G., and O. Ramaré. "Errata to "Average orders of multiplicative arithmetical functions of integer matrices" (Acta Arith. 66 (1994), 45-62)." Acta Arithmetica 85, no. 1 (1998): 97–98. http://dx.doi.org/10.4064/aa-85-1-97-98.

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28

Lagarias, Jeffrey C. "Correction to: ``On a positivity property of the Riemann ξ-function'' (Acta Arith. 89 (1999), 217–234)". Acta Arithmetica 116, № 3 (2005): 293–94. http://dx.doi.org/10.4064/aa116-3-5.

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29

Faure, Henri, and Christiane Lemieux. "Corrigendum to: ``Improvements on the star discrepancy of (t,s)-sequences" (Acta Arith. 154 (2012), 61–78)." Acta Arithmetica 159, no. 3 (2013): 299–300. http://dx.doi.org/10.4064/aa159-3-5.

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30

Larcher, Gerhard. "Corrigendum to the paper "On the distribution of s-dimensional Kronecker sequences" Acta Arith. 51 (1988), 335-347." Acta Arithmetica 60, no. 1 (1991): 93–95. http://dx.doi.org/10.4064/aa-60-1-93-95.

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31

Raouj, A. "Correction au travail "Sur la densité de certains ensembles de multiples, 1", (Acta Arith. 69 (1995), 121-152)." Acta Arithmetica 83, no. 2 (1998): 197–98. http://dx.doi.org/10.4064/aa-83-2-197-198.

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32

Poulakis, Dimitrios. "Corrigendum to the paper "The number of solutions of the Mordell equation" (Acta Arith. 88 (1999), 173–179)." Acta Arithmetica 92, no. 4 (2000): 387–88. http://dx.doi.org/10.4064/aa-92-4-387-388.

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33

Tolev, D. I. "Corrigendum to the paper ``Additive problems with prime numbers of special type'' (Acta Arith. 96 (2000), 53–88)." Acta Arithmetica 105, no. 2 (2002): 205. http://dx.doi.org/10.4064/aa105-2-7.

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34

Pong, Wai Yan. "Addendum to ``Applications of differential algebra to algebraic independence of arithmetic functions'' (Acta Arith. 172 (2016), 149--173)." Acta Arithmetica 196, no. 3 (2020): 325–27. http://dx.doi.org/10.4064/aa200210-14-7.

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35

Urban, Roman. "Corrigendum to ``On density modulo 1 of some expressions containing algebraic integers'' (Acta Arith. 127 (2007), 217–229)." Acta Arithmetica 141, no. 2 (2010): 209–10. http://dx.doi.org/10.4064/aa141-2-5.

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36

Bremner, Andrew. "On a problem of Erdös related to common factor differences." International Journal of Number Theory 15, no. 05 (2019): 1059–68. http://dx.doi.org/10.1142/s1793042119500581.

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Let [Formula: see text] be a positive integer. The factor-difference set [Formula: see text] of [Formula: see text] is the set of absolute values [Formula: see text] of the differences between the factors of any factorization of [Formula: see text] as a product of two integers. Erdős and Rosenfeld [The factor–difference set of integers, Acta Arith. 79(4) (1997) 353–359] ask whether for every positive integer [Formula: see text] there exist integers [Formula: see text] such that [Formula: see text], and prove this is true when [Formula: see text]. Urroz [A note on a conjecture of Erdős and Rose

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37

Carletti, E., and G. Monti Bragadin. "Errata to the paper "On a functional equation satisfied by certain Dirichlet series" (Acta Arith. 71 (1995), 265-272)." Acta Arithmetica 82, no. 1 (1997): 99–101. http://dx.doi.org/10.4064/aa-82-1-99-101.

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38

Zannier, Umberto. "Addendum to the paper: ``On the number of terms of a composite polynomial'' (Acta Arith. 127 (2007), 157–167)." Acta Arithmetica 140, no. 1 (2009): 93–99. http://dx.doi.org/10.4064/aa140-1-6.

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39

Ayad, Mohamed, and Donald L. McQuillan. "Corrections to ``Irreducibility of the iterates of a quadratic polynomial over a field'' (Acta Arith. 93 (2000), 87–97)." Acta Arithmetica 99, no. 1 (2001): 97. http://dx.doi.org/10.4064/aa99-1-9.

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40

Zhu, H. L. "Corrigendum to the paper ``A note on the Diophantine equation x2+qm=y3'' (Acta Arith. 146 (2011), 195–202)." Acta Arithmetica 152, no. 4 (2012): 425–26. http://dx.doi.org/10.4064/aa152-4-5.

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41

Schinzel, A. "Corrigendum to the paper ``On the greatest common divisor of two univariate polynomials, II'' (Acta Arith. 98 (2001), 95–106)." Acta Arithmetica 115, no. 4 (2004): 403. http://dx.doi.org/10.4064/aa115-4-4.

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42

Pacheco, Amílcar. "Corrigendum to ``Distribution of the traces of Frobenius on elliptic curves over function fields'' (Acta Arith. 106 (2003), 255–263)." Acta Arithmetica 142, no. 2 (2010): 197–98. http://dx.doi.org/10.4064/aa142-2-9.

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43

Saradha, N., T. Shorey, and R. Tijdeman. "Corrections to the paper "On values of a polynomial a arithmetic progressions with equal products" (Acta Arith. 72 (1995), 67-76)." Acta Arithmetica 84, no. 4 (1998): 385–86. http://dx.doi.org/10.4064/aa-84-4-385-386.

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44

Chakri, Lekbir, and El Mostafa Hanine. "Correction of ``Polynômes singuliers à plusieurs variables sur un corps fini et congruences modulo p2'' (Acta Arith. 68 (1994), 1–10)." Acta Arithmetica 100, no. 4 (2001): 391–96. http://dx.doi.org/10.4064/aa100-4-7.

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45

Kimura, Iwao. "Correction to ``A note on the existence of certain infinite families of imaginary quadratic fields'' (Acta Arith. 110 (2003), 37–43)." Acta Arithmetica 114, no. 4 (2004): 397. http://dx.doi.org/10.4064/aa114-4-8.

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46

Steuding, Jörn, and Annegret Weng. "Erratum: ``On the number of prime divisors of the order of elliptic curves modulo p'' (Acta Arith. 117 (2005), 341–352)." Acta Arithmetica 119, no. 4 (2005): 407–8. http://dx.doi.org/10.4064/aa119-4-6.

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47

Zhu, Wenbin. "Erratum to “Representation of integers as sums of fractional powers of primes and powers of 2” (Acta Arith. 181 (2017), 185–196)." Acta Arithmetica 185, no. 2 (2018): 197–99. http://dx.doi.org/10.4064/aa180327-18-8.

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48

Tengely, Sz. "Note on the paper ``An extension of a theorem of Euler" by Hirata-Kohno et al. (Acta Arith. 129 (2007), 71–102)." Acta Arithmetica 134, no. 4 (2008): 329–35. http://dx.doi.org/10.4064/aa134-4-3.

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49

Hopkins, Christopher D., Mary Anne Raymond, and Les Carlson. "Educating Students to Give Them a Sustainable Competitive Advantage." Journal of Marketing Education 33, no. 3 (2011): 337–47. http://dx.doi.org/10.1177/0273475311420241.

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With an increasingly competitive job market, this study focuses on what marketing educators can do to help students develop a sustainable competitive advantage. The authors conducted a survey of students, faculty, and recruiters to develop a better understanding of what skills and characteristics might be of value to each group of respondents and to ascertain where differences might exist across respondent groups. Although the basic skills (i.e., critical thinking, communication) recruiters seek have not changed much from previous studies, recruiters rated critical thinking skills, such as pro

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50

Laurinčikas, Antanas. "Corrigendum to the paper ``Limit theorems for the Mellin transform of the square of the Riemann zeta-function. I" (Acta Arith. 122 (2006), 173–184)." Acta Arithmetica 143, no. 2 (2010): 191–95. http://dx.doi.org/10.4064/aa143-2-3.

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