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136 publications using GAP in the category "Number theory"

[A97] Adler, A., The Mathieu group $M_11$ and the modular curve $X(11)$, Proc. London Math. Soc. (3), 74 (1) (1997), 1--28.

[AG08] Aguglia, A. and Giuzzi, L., Construction of a 3-dimensional MDS-code, Contrib. Discrete Math., 3 (1) (2008), 39--46.

[AG10] Aguiló-Gost, F. and Garc\'\ia-Sánchez, P. A., Factoring in embedding dimension three numerical semigroups, Electron. J. Combin., 17 (1) (2010), Research Paper 138, 21.

[AH16] Araya, M. and Harada, M., On the classification of certain ternary codes of length 12, Hiroshima Math. J., 46 (1) (2016), 87--96.

[A07] Asaeda, M., Galois groups and an obstruction to principal graphs of subfactors, Internat. J. Math., 18 (2) (2007), 191--202.

[APS05] Ash, A., Pollack, D., and Sinnott, W., $A_6$-extensions of $\Bbb Q$ and the mod $p$ cohomology of $\rm GL_3(\Bbb Z)$, J. Number Theory, 115 (1) (2005), 176--196.

[AT+16] Azizi, A., Talbi, M., Talbi, M., Derhem, A., and Mayer, D. C., The group $\textGal(k_3^(2)\vert k)$ for $k=\BbbQ(\sqrt-3,\sqrtd)$ of type $(3,3)$, Int. J. Number Theory, 12 (7) (2016), 1951--1986.

[B06] Bailey, R. F., Uncoverings-by-bases for base-transitive permutation groups, Des. Codes Cryptogr., 41 (2) (2006), 153--176.

[BD14] Baishya, S. J. and Das, A. K., Harmonic numbers and finite groups, Rend. Semin. Mat. Univ. Padova, 132 (2014), 33--43.

[B00] Bartholdi, L., Lamps, factorizations, and finite fields, Amer. Math. Monthly, 107 (5) (2000), 429--436.

[BB+15] Bartholdi, L., Buff, X., Graf von Bothmer, H., and Kröker, J., Algorithmic construction of Hurwitz maps, Exp. Math., 24 (1) (2015), 76--92.

[BB07] Bartholdi, L. and Bush, M. R., Maximal unramified 3-extensions of imaginary quadratic fields and $\rm SL_2(\Bbb Z_3)$, J. Number Theory, 124 (1) (2007), 159--166.

[BH10] Bartholdi, L. and de la Harpe, P., Representation zeta functions of wreath products with finite groups, Groups Geom. Dyn., 4 (2) (2010), 209--249.

[BGP11] Blanco, V., Garc\'\ia-Sánchez, P. A., and Puerto, J., Counting numerical semigroups with short generating functions, Internat. J. Algebra Comput., 21 (7) (2011), 1217--1235.

[BP12] Blanco, V. and Puerto, J., An application of integer programming to the decomposition of numerical semigroups, SIAM J. Discrete Math., 26 (3) (2012), 1210--1237.

[BB04] Bley, W. and Boltje, R., Cohomological Mackey functors in number theory, J. Number Theory, 105 (1) (2004), 1--37.

[B06] Booker, A. R., Artin's conjecture, Turing's method, and the Riemann hypothesis, Experiment. Math., 15 (4) (2006), 385--407.

[B16] Bors, A., Classification of finite group automorphisms with a large cycle, Comm. Algebra, 44 (11) (2016), 4823--4843.

[BMV15] Brai\'c, S., Mandi\'c, J., and Vu\vci\vci\'c, T., Primitive block designs with automorphism group $\rm PSL(2,q)$, Glas. Mat. Ser. III, 50(70) (1) (2015), 1--15.

[BP00] Bratus, S. and Pak, I., Fast constructive recognition of a black box group isomorphic to $S_n$ or $A_n$ using Goldbach's conjecture, J. Symbolic Comput., 29 (1) (2000), 33--57.

[B97] Breuer, T., Integral bases for subfields of cyclotomic fields, Appl. Algebra Engrg. Comm. Comput., 8 (4) (1997), 279--289.

[BG13] Browkin, J. and Gangl, H., Tame kernels and second regulators of number fields and their subfields, J. K-Theory, 12 (1) (2013), 137--165.

[B12] Butske, W., Endomorphisms of two dimensional Jacobians and related finite algebras, Canad. Math. Bull., 55 (1) (2012), 38--47.

[CD06] Calegari, F. and Dunfield, N. M., Automorphic forms and rational homology 3-spheres, Geom. Topol., 10 (2006), 295--329 (electronic).

[CC+04] Campbell, C. M., Campbell, P. P., Doostie, H., and Robertson, E. F., On the Fibonacci length of powers of dihedral groups, in Applications of Fibonacci numbers. Vol. 9, Kluwer Acad. Publ., Dordrecht (2004), 69--85.

[C13] Cao, W., Degree matrices and estimates for exponential sums of polynomials over finite fields, J. Algebra Appl., 12 (7) (2013), 1350030, 9.

[C09] Cao, W., Smith normal form of augmented degree matrix and its applications, Linear Algebra Appl., 431 (10) (2009), 1778--1784.

[CO01] Caprotti, O. and Oostdijk, M., Formal and efficient primality proofs by use of computer algebra oracles, J. Symbolic Comput., 32 (1-2) (2001), 55--70
(Computer algebra and mechanized reasoning (St. Andrews, 2000)).

[C03] Cardona, G., On the number of curves of genus 2 over a finite field, Finite Fields Appl., 9 (4) (2003), 505--526.

[CM08] Carlip, W. and Mincheva, M., Symmetry of iteration graphs, Czechoslovak Math. J., 58(133) (1) (2008), 131--145.

[CS07] Carlip, W. and Somer, L., Primitive Lucas $d$-pseudoprimes and Carmichael-Lucas numbers, Colloq. Math., 108 (1) (2007), 73--92.

[CC99] Carnahan, S. and Childs, L., Counting Hopf Galois structures on non-abelian Galois field extensions, J. Algebra, 218 (1) (1999), 81--92.

[CGL09] Chapman, S. T., Garc\'\ia-Sánchez, P. A., and Llena, D., The catenary and tame degree of numerical monoids, Forum Math., 21 (1) (2009), 117--129.

[CG+11] Chapman, S. T., Garc\'\ia-Sánchez, P. A., Llena, D., and Marshall, J., Elements in a numerical semigroup with factorizations of the same length, Canad. Math. Bull., 54 (1) (2011), 39--43.

[CGP14] Chapman, S. T., Gotti, F., and Pelayo, R., On delta sets and their realizable subsets in Krull monoids with cyclic class groups, Colloq. Math., 137 (1) (2014), 137--146.

[CDH14] Cheng, M. C. N., Duncan, J. F. R., and Harvey, J. A., Umbral moonshine, Commun. Number Theory Phys., 8 (2) (2014), 101--242.

[CH+15] Chu, H., Hoshi, A., Hu, S., and Kang, M., Noether's problem for groups of order 243, J. Algebra, 442 (2015), 233--259.

[C05] Chua, K. S., Extremal modular lattices, McKay Thompson series, quadratic iterations, and new series for $\pi$, Experiment. Math., 14 (3) (2005), 343--357.

[CLY04] Chua, K. S., Lang, M. L., and Yang, Y., On Rademacher's conjecture: congruence subgroups of genus zero of the modular group, J. Algebra, 277 (1) (2004), 408--428.

[CGS12] Cicalò, S., de Graaf, W. A., and Schneider, C., Six-dimensional nilpotent Lie algebras, Linear Algebra Appl., 436 (1) (2012), 163--189.

[CGM16] Ciolan, E., Garc\'\ia-Sánchez, P. A., and Moree, P., Cyclotomic numerical semigroups, SIAM J. Discrete Math., 30 (2) (2016), 650--668.

[C93] Cohen, H., A course in computational algebraic number theory, Springer-Verlag, Berlin, Graduate Texts in Mathematics, 138 (1993), xii+534 pages.

[CJ+13] Conder, M. D. E., Jones, G. A., Streit, M., and Wolfart, J., Galois actions on regular dessins of small genera, Rev. Mat. Iberoam., 29 (1) (2013), 163--181.

[CKK01] Cornelissen, G., Kato, F., and Kontogeorgis, A., Discontinuous groups in positive characteristic and automorphisms of Mumford curves, Math. Ann., 320 (1) (2001), 55--85.

[DF+97] Daberkow, M., Fieker, C., Klüners, J., Pohst, M., Roegner, K., Schörnig, M., and Wildanger, K., KANT V4, J. Symbolic Comput., 24 (3-4) (1997), 267--283
(Computational algebra and number theory (London, 1993)).

[DH+16] De Beule, J., Héger, T., Szőnyi, T., and Van de Voorde, G., Blocking and double blocking sets in finite planes, Electron. J. Combin., 23 (2) (2016), Paper 2.5, 21.

[GP09] de Graaf, W. A. and Pavan, A., Constructing arithmetic subgroups of unipotent groups, J. Algebra, 322 (11) (2009), 3950--3970.

[D12] Degtyarev, A., Topology of algebraic curves, Walter de Gruyter \& Co., Berlin, De Gruyter Studies in Mathematics, 44 (2012), xvi+393 pages
(An approach via dessins d'enfants).

[DR14] Dejou, G. and Roblot, X., A Brumer-Stark conjecture for non-abelian Galois extensions, J. Number Theory, 142 (2014), 51--88.

[DF+13] Delgado, M., Farrán, J. I., Garc\'\ia-Sánchez, P. A., and Llena, D., On the generalized Feng-Rao numbers of numerical semigroups generated by intervals, Math. Comp., 82 (283) (2013), 1813--1836.

[DGR16] Delgado, M., Garc\'\ia-Sánchez, P. A., and Robles-Pérez, A. M., Numerical semigroups with a given set of pseudo-Frobenius numbers, LMS J. Comput. Math., 19 (1) (2016), 186--205.

[DG+08] Delgado, M., Garc\'\ia-Sánchez, P. A., Rosales, J. C., and Urbano-Blanco, J. M., Systems of proportionally modular Diophantine inequalities, Semigroup Forum, 76 (3) (2008), 469--488.

[DR06] Delgado, M. and Rosales, J. C., On the Frobenius number of a proportionally modular Diophantine inequality, Port. Math. (N.S.), 63 (4) (2006), 415--425.

[DKC10] Deveci, O., Karaduman, E., and Campbell, C. M., The periods of $k$-nacci sequences in centro-polyhedral groups and related groups, Ars Combin., 97A (2010), 193--210.

[DGH98] Dong, C., Griess Jr. , R. L., and Höhn, G., Framed vertex operator algebras, codes and the Moonshine module, Comm. Math. Phys., 193 (2) (1998), 407--448.

[DJ15] Dubickas, A. and Jankauskas, J., Simple linear relations between conjugate algebraic numbers of low degree, J. Ramanujan Math. Soc., 30 (2) (2015), 219--235.

[DER07] Dutour, M., Erdahl, R., and Rybnikov, K., Perfect Delaunay polytopes in low dimensions, Integers, 7 (2007), A39, 49.

[DES11] Dutour Sikiri\'c, M., Ellis, G., and Schürmann, A., On the integral homology of $\rm PSL_4(\Bbb Z)$ and other arithmetic groups, J. Number Theory, 131 (12) (2011), 2368--2375.

[DG+16] Dutour Sikiri\'c, M., Gangl, H., Gunnells, P. E., Hanke, J., Schürmann, A., and Yasaki, D., On the cohomology of linear groups over imaginary quadratic fields, J. Pure Appl. Algebra, 220 (7) (2016), 2564--2589.

[EGS13] Elbaz-Vincent, P., Gangl, H., and Soulé, C., Perfect forms, K-theory and the cohomology of modular groups, Adv. Math., 245 (2013), 587--624.

[EG+08] Estrada, S., Garc\'\ia-Rozas, J. R., Peralta, J., and Sánchez-Garc\'\ia, E., Group convolutional codes, Adv. Math. Commun., 2 (1) (2008), 83--94.

[FK03] Fieker, C. and Klüners, J., Minimal discriminants for fields with small Frobenius groups as Galois groups, J. Number Theory, 99 (2) (2003), 318--337.

[FL13] Fité, F. and Lario, J., The twisting representation of the $L$-function of a curve, Rev. Mat. Iberoam., 29 (3) (2013), 749--764.

[FS04] Freitag, E. and Salvati Manni, R., The Burkhardt group and modular forms, Transform. Groups, 9 (1) (2004), 25--45.

[GP+13] Gaberdiel, M. R., Persson, D., Ronellenfitsch, H., and Volpato, R., Generalized Mathieu Moonshine, Commun. Number Theory Phys., 7 (1) (2013), 145--223.

[GG14] Gal, I. and Grizzard, R., On the compositum of all degree $d$ extensions of a number field, J. Théor. Nombres Bordeaux, 26 (3) (2014), 655--673.

[GY13] Geroldinger, A. and Yuan, P., The monotone catenary degree of Krull monoids, Results Math., 63 (3-4) (2013), 999--1031.

[GH09] Giudici, M. and Hart, S., Small maximal sum-free sets, Electron. J. Combin., 16 (1) (2009), Research Paper 59, 17.

[GHT15] Guralnick, R., Herzig, F., and Tiep, P. H., Adequate groups of low degree, Algebra Number Theory, 9 (1) (2015), 77--147.

[H12] Hashimoto, K., Finite symplectic actions on the $K3$ lattice, Nagoya Math. J., 206 (2012), 99--153.

[HMM98] Havas, G., Majewski, B. S., and Matthews, K. R., Extended GCD and Hermite normal form algorithms via lattice basis reduction, Experiment. Math., 7 (2) (1998), 125--136.

[HMR13] He, Y., McKay, J., and Read, J., Modular subgroups, \it dessins d'enfants and elliptic K3 surfaces, LMS J. Comput. Math., 16 (2013), 271--318.

[HL04] Heath, L. S. and Loehr, N. A., New algorithms for generating Conway polynomials over finite fields, J. Symbolic Comput., 38 (2) (2004), 1003--1024.

[H07] Helfgott, H. A., Power-free values, large deviations and integer points on irrational curves, J. Théor. Nombres Bordeaux, 19 (2) (2007), 433--472.

[H04] Helfgott, H. A., On the square-free sieve, Acta Arith., 115 (4) (2004), 349--402.

[HS15] Hofmann, J. and van Straten, D., Some monodromy groups of finite index in $Sp_4(\BbbZ)$, J. Aust. Math. Soc., 99 (1) (2015), 48--62.

[H12] Hoshi, A., On the simplest sextic fields and related Thue equations, Funct. Approx. Comment. Math., 47 (part 1) (2012), 35--49.

[HM10] Hoshi, A. and Miyake, K., On the field intersection problem of solvable quintic generic polynomials, Int. J. Number Theory, 6 (5) (2010), 1047--1081.

[HKP10] Huang, P., Ke, W., and Pilz, G. F., The cardinality of some symmetric differences, Proc. Amer. Math. Soc., 138 (3) (2010), 787--797.

[H14] Huczynska, S., Beyond sum-free sets in the natural numbers, Electron. J. Combin., 21 (1) (2014), Paper 1.21, 20.

[H07] Huffman, W. C., On the decomposition of self-dual codes over $\Bbb F_2+u\Bbb F_2$ with an automorphism of odd prime order, Finite Fields Appl., 13 (3) (2007), 681--712.

[H99] Hulpke, A., Galois groups through invariant relations, in Groups St. Andrews 1997 in Bath, II, Cambridge Univ. Press, Cambridge, London Math. Soc. Lecture Note Ser., 261 (1999), 379--393.

[H13] Hulpke, A., Computing generators of groups preserving a bilinear form over residue class rings, J. Symbolic Comput., 50 (2013), 298--307.

[J11] Jones, J. W., Wild ramification bounds and simple group Galois extensions ramified only at 2, Proc. Amer. Math. Soc., 139 (3) (2011), 807--821.

[J10] Jones, J. W., Number fields unramified away from 2, J. Number Theory, 130 (6) (2010), 1282--1291.

[J13] Jones, J. W., Minimal solvable nonic fields, LMS J. Comput. Math., 16 (2013), 130--138.

[JR14] Jones, J. W. and Roberts, D. P., A database of number fields, LMS J. Comput. Math., 17 (1) (2014), 595--618.

[JR08] Jones, J. W. and Roberts, D. P., Octic 2-adic fields, J. Number Theory, 128 (6) (2008), 1410--1429.

[JW12] Jones, J. W. and Wallington, R., Number fields with solvable Galois groups and small Galois root discriminants, Math. Comp., 81 (277) (2012), 555--567.

[KP06] Karve, A. and Pauli, S., GiANT: graphical algebraic number theory, J. Théor. Nombres Bordeaux, 18 (3) (2006), 721--727.

[K04] Katz, N. M., Notes on $G_2$, determinants, and equidistribution, Finite Fields Appl., 10 (2) (2004), 221--269.

[K07] Katz, N. M., $G_2$ and hypergeometric sheaves, Finite Fields Appl., 13 (2) (2007), 175--223.

[K07] Kedlaya, K. S., Mass formulas for local Galois representations, Int. Math. Res. Not. IMRN (17) (2007), Art. ID rnm021, 26
(With an appendix by Daniel Gulotta).

[KOP16] Kiers, C., O'Neill, C., and Ponomarenko, V., Numerical semigroups on compound sequences, Comm. Algebra, 44 (9) (2016), 3842--3852.

[KSV11] Kiming, I., Schütt, M., and Verrill, H. A., Lifts of projective congruence groups, J. Lond. Math. Soc. (2), 83 (1) (2011), 96--120.

[K07] Kohl, S., Wildness of iteration of certain residue-class-wise affine mappings, Adv. in Appl. Math., 39 (3) (2007), 322--328.

[K08] Kohl, S., On conjugates of Collatz-type mappings, Int. J. Number Theory, 4 (1) (2008), 117--120.

[KN13] Korchmáros, G. and Nagy, G. P., Hermitian codes from higher degree places, J. Pure Appl. Algebra, 217 (12) (2013), 2371--2381.

[KN13] Korchmáros, G. and Nagy, G. P., Lower bounds on the minimum distance in Hermitian one-point differential codes, Sci. China Math., 56 (7) (2013), 1449--1455.

[LP02] Lansky, J. and Pollack, D., Hecke algebras and automorphic forms, Compositio Math., 130 (1) (2002), 21--48.

[L14] Leshin, J., Solvable Artin representations ramified at one prime, Bull. Lond. Math. Soc., 46 (1) (2014), 59--75.

[LW99] Lindenbergh, R. C. and van der Waall, R. W., Ergebnisse über Dedekind-Zeta-Funktionen, monomiale Charaktere und Konjugationsklassen endlicher Gruppen, unter Benutzung von GAP, Bayreuth. Math. Schr. (56) (1999), 79--148.

[M04] Martin, K., Modularity of hypertetrahedral representations, C. R. Math. Acad. Sci. Paris, 339 (2) (2004), 99--102.

[M03] Martin, K., A symplectic case of Artin's conjecture, Math. Res. Lett., 10 (4) (2003), 483--492.

[M13] Mayer, D. C., The distribution of second $p$-class groups on coclass graphs, J. Théor. Nombres Bordeaux, 25 (2) (2013), 401--456.

[M14] Mayer, D. C., Principalization algorithm via class group structure, J. Théor. Nombres Bordeaux, 26 (2) (2014), 415--464.

[M98] Müller, P., Kronecker conjugacy of polynomials, Trans. Amer. Math. Soc., 350 (5) (1998), 1823--1850.

[N00] Nebe, G., Invariants of orthogonal $G$-modules from the character table, Experiment. Math., 9 (4) (2000), 623--629.

[N98] Nebe, G., Finite quaternionic matrix groups, Represent. Theory, 2 (1998), 106--223 (electronic).

[NP95] Nebe, G. and Plesken, W., Finite rational matrix groups, Mem. Amer. Math. Soc., 116 (556) (1995), viii+144.

[N15] Nikulin, V. V., Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups, Izv. Ross. Akad. Nauk Ser. Mat., 79 (4) (2015), 103--158.

[N07] Nomura, A., A note on the 3-class field tower of a cyclic cubic field, Proc. Japan Acad. Ser. A Math. Sci., 83 (2) (2007), 14--15.

[N08] Nomura, A., Notes on the minimal number of ramified primes in some $l$-extensions of $\bf Q$, Arch. Math. (Basel), 90 (6) (2008), 501--510.

[OS97] Omrani, A. and Shokrollahi, A., Computing irreducible representations of supersolvable groups over small finite fields, Math. Comp., 66 (218) (1997), 779--786.

[OP15] O'Neill, C. and Pelayo, R., How do you measure primality?, Amer. Math. Monthly, 122 (2) (2015), 121--137.

[OP14] O'Neill, C. and Pelayo, R., On the linearity of $\omega$-primality in numerical monoids, J. Pure Appl. Algebra, 218 (9) (2014), 1620--1627.

[O97] Oura, M., The dimension formula for the ring of code polynomials in genus $4$, Osaka J. Math., 34 (1) (1997), 53--72.

[PK07] Park, S. and Kwon, S., Class number one problem for normal CM-fields, J. Number Theory, 125 (1) (2007), 59--84.

[P08] Paulhus, J., Decomposing Jacobians of curves with extra automorphisms, Acta Arith., 132 (3) (2008), 231--244.

[PS10] Pernet, C. and Stein, W., Fast computation of Hermite normal forms of random integer matrices, J. Number Theory, 130 (7) (2010), 1675--1683.

[PP93] Plesken, W. and Pohst, M., Constructing integral lattices with prescribed minimum. II, Math. Comp., 60 (202) (1993), 817--825.

[R05] Rattaggi, D., Anti-tori in square complex groups, Geom. Dedicata, 114 (2005), 189--207.

[R00] Reeder, M., Formal degrees and $L$-packets of unipotent discrete series representations of exceptional $p$-adic groups, J. Reine Angew. Math., 520 (2000), 37--93
(With an appendix by Frank Lübeck).

[R15] Rossmann, T., Computing topological zeta functions of groups, algebras, and modules, II, J. Algebra, 444 (2015), 567--605.

[S10] Sawa, M., Optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4, IEEE Trans. Inform. Theory, 56 (7) (2010), 3613--3620.

[S10] Schürmann, A., Perfect, strongly eutactic lattices are periodic extreme, Adv. Math., 225 (5) (2010), 2546--2564.

[SSV07] Sikiri\'c, M. D., Schürmann, A., and Vallentin, F., Classification of eight-dimensional perfect forms, Electron. Res. Announc. Amer. Math. Soc., 13 (2007), 21--32 (electronic).

[SZ05] Silverberg, A. and Zarhin, Y. G., Inertia groups and abelian surfaces, J. Number Theory, 110 (1) (2005), 178--198.

[S13] Soda\"\igui, B., Classes de Steinitz d'extensions galoisiennes à groupe de Galois un 2-groupe, Funct. Approx. Comment. Math., 48 (part 2) (2013), 183--196.

[S94] Souvignier, B., Irreducible finite integral matrix groups of degree $8$ and $10$, Math. Comp., 63 (207) (1994), 335--350
(With microfiche supplement).

[T99] Terras, A., Fourier analysis on finite groups and applications, Cambridge University Press, Cambridge, London Mathematical Society Student Texts, 43 (1999), x+442 pages.

[T04] Totaro, B., Splitting fields for $E_8$-torsors, Duke Math. J., 121 (3) (2004), 425--455.

[U13] Ugolini, S., Graphs associated with the map $X\mapsto X+X^-1$ in finite fields of characteristic three and five, J. Number Theory, 133 (4) (2013), 1207--1228.

[U15] Ugolini, S., Sequences of irreducible polynomials over odd prime fields via elliptic curve endomorphisms, J. Number Theory, 152 (2015), 21--37.

[V08] Valibouze, A., Sur les relations entre les racines d'un polyn\^ome, Acta Arith., 131 (1) (2008), 1--27.

[S05] \vSuch, O., On families of additive exponential sums, Finite Fields Appl., 11 (4) (2005), 700--723.