Average order in cyclic groups

Authors: Florian Luca, Lutz G. Lucht, Arnold Knopfmacher, Igor E. Shparlinski, Joachim von zur Gathen

Source: Journal de théorie des nombres de Bordeaux. 16:107-123

Subject Terms: Other results on the distribution of values or the characterization of arithmetic functions, 0301 basic medicine, 03 medical and health sciences, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://jtnb.centre-mersenne.org/item/10.5802/jtnb.436.pdf
http://www.numdam.org/item/10.5802/jtnb.436.pdf
https://jtnb.centre-mersenne.org/item/10.5802/jtnb.436.pdf
http://www.numdam.org/item/JTNB_2004__16_1_107_0/
http://www.numdam.org/item?id=JTNB_2004__16_1_107_0
http://jtnb.cedram.org/item?id=JTNB_2004__16_1_107_0
http://almira.math.u-bordeaux1.fr/jtnb/2004-1/GathenKnopfmacherLucaLuchtSchparlinsky.pdf

Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields: Some mean values related to average multiplicative orders of elements in finite fields

Authors: Florian Luca

Source: The Ramanujan Journal. 9:33-44

Subject Terms: Euler's phi function, enumeration problems, Asymptotic results on counting functions for algebraic and topological structures, cyclic groups, finite fields, asymptotic estimates, 0101 mathematics, average order, Asymptotic enumeration, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s11139-005-0823-7

On the distribution of algebraic numbers with prescribed factorization properties

Authors: Maciej Radziejewski

Source: Acta Arithmetica. 116:153-171

Subject Terms: Selberg class, error terms, oscillations, Asymptotic results on arithmetic functions, Zeta functions and \(L\)-functions of number fields, functional independence, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, Units and factorization, Mellin transforms, factorizations of distinct lengths, 01 natural sciences, Hilbert semigroup

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https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/116/2/82119/on-the-distribution-of-algebraic-numbers-with-prescribed-factorization-properties
https://www.impan.pl/shop/publication/transaction/download/product/82119?download.pdf
http://ui.adsabs.harvard.edu/abs/2005AcAri.116..153R/abstract
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa116-2-4
http://journals.impan.pl/cgi-bin/doi?aa116-2-4

Counting invertible matrices and uniform distribution

Authors: Christian Roettger

Source: Journal de Théorie des Nombres de Bordeaux. 17:301-322

Subject Terms: uniform distribution, Algebraic number theory: global fields, counting problems, matrices, Distribution modulo one, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, Matrices, determinants in number theory, 01 natural sciences

File Description: application/xml

Access URL: http://almira.math.u-bordeaux.fr/jtnb/2005-1/pages301-322.pdf
https://zbmath.org/2205447
https://doi.org/10.5802/jtnb.492
https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.492/
https://jtnb.centre-mersenne.org/item/10.5802/jtnb.492.pdf
https://eudml.org/doc/249421
http://core.ac.uk/display/23349824

Word maps have large image: Word maps have large image.

Authors: Michael Larsen

Source: Israel Journal of Mathematics. 139:149-156

Subject Terms: 20G15, word maps, dominant morphisms, 20D06, Group Theory (math.GR), 01 natural sciences, Linear algebraic groups over arbitrary fields, finite simple groups, FOS: Mathematics, semisimple algebraic groups, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, Mathematics - Group Theory

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0211302
http://arxiv.org/abs/math/0211302
https://zbmath.org/2114525
https://doi.org/10.1007/bf02787545
https://www.arxiv-vanity.com/papers/math/0211302/
https://link.springer.com/article/10.1007/BF02787545

Estimates of convolutions of certain number‐theoretic error terms: Estimates of convolutions of certain number-theoretic error terms

Authors: Aleksandar Ivić

Source: International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 1, Pp 1-23 (2004)

Subject Terms: Piltz divisor problem, 0301 basic medicine, nonisomorphic Abelian groups, 01 natural sciences, asymptotic results on arithmetic functions, 03 medical and health sciences, \(\zeta (s)\) and \(L(s, \chi)\), QA1-939, Asymptotic results on arithmetic functions, Special integral transforms (Legendre, Hilbert, etc.), Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, Mathematics, Mellin transform, Riemann zeta-function, Rankin-Selberg convolution

File Description: application/xml

Access URL: https://downloads.hindawi.com/journals/ijmms/2004/317515.pdf
https://zbmath.org/2168594
https://doi.org/10.1155/s0161171204305156
https://doaj.org/article/94770b74ef95482aa9da97480fb80331
https://downloads.hindawi.com/journals/ijmms/2004/317515.pdf
https://dblp.uni-trier.de/db/journals/ijmmsc/ijmmsc2004.html#Ivic04
http://emis.maths.adelaide.edu.au/journals/HOA/IJMMS/Volume2004_1/23.pdf
https://www.hindawi.com/journals/ijmms/2004/317515/
http://downloads.hindawi.com/journals/ijmms/2004/317515.pdf
https://www.maths.tcd.ie/EMIS/journals/HOA/IJMMS/2004/1-41.pdf

Counting congruence subgroups: Counting congruence subgroups.

Authors: Goldfeld, Dorian, Lubotzky, Alexander, Pyber, László

Source: Acta Math. 193, no. 1 (2004), 73-104

Subject Terms: Unimodular groups, congruence subgroups (group-theoretic aspects), numbers of subgroups, Subgroup theorems, subgroup growth, algebraic number fields, modular group, Structure of modular groups and generalizations, arithmetic groups, rings of integers, Group Theory (math.GR), Discrete subgroups of Lie groups, semisimple simply-connected connected algebraic groups, 01 natural sciences, Riemann surfaces, 0103 physical sciences, congruence subgroups, FOS: Mathematics, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, Mathematics - Group Theory

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/math/0406249
https://www.math.columbia.edu/~goldfeld/Goldfeld-Lubotzky-Pyber.pdf
https://link.springer.com/content/pdf/10.1007/BF02392551.pdf
https://projecteuclid.org/download/pdf_1/euclid.acta/1485891669
https://projecteuclid.org/journals/acta-mathematica/volume-193/issue-1/Counting-congruence-subgroups/10.1007/BF02392551.full
https://link.springer.com/article/10.1007/BF02392551
https://dialnet.unirioja.es/servlet/articulo?codigo=1083518
http://projecteuclid.org/euclid.acta/1485891669

Normal growth of large groups: Normal growth of large groups.

Authors: Thomas Müller, Jan-Christoph Schlage-Puchta

Source: Archiv der Mathematik. 81:609-613

Subject Terms: Generators, relations, and presentations of groups, subgroups of finite index, Subgroup theorems, subgroup growth, 0102 computer and information sciences, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, finitely generated groups, 01 natural sciences, normal subgroup growth

File Description: application/xml

Access URL: https://zbmath.org/2051644
https://doi.org/10.1007/s00013-003-4768-z
https://link.springer.com/article/10.1007%2Fs00013-003-4768-z
https://core.ac.uk/display/55795795
http://www.math.uni-rostock.de/~schlage-puchta/papers/NormalgrowthI.pdf
https://biblio.ugent.be/publication/597053

On the zetafunction of an arithmetical semigroup: On the zeta-function of an arithmetical semigroup

Authors: Richard Warlimont

Source: Mathematische Zeitschrift. 245:419-434

Subject Terms: zetafunction, arithmetical semigroup, 0102 computer and information sciences, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, Asymptotic enumeration, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1007%2Fs00209-003-0534-y.pdf
https://documat.unirioja.es/servlet/articulo?codigo=2806670
https://dialnet.unirioja.es/servlet/articulo?codigo=2806670
https://link.springer.com/article/10.1007/s00209-003-0534-y

A Multiplicative Analogue of Schur's Tauberian Theorem: A multiplicative analogue of Schur's Tauberian theorem

Authors: Karen Yeats

Source: Canadian Mathematical Bulletin. 46:473-480

Subject Terms: Tauberian theorems, convolution of Dirichlet series, regularly varying measurable functions, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, 16. Peace & justice, 01 natural sciences

File Description: application/xml

Access URL: https://cms.math.ca/cmb/abstract/pdf/149509.pdf
https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/multiplicative-analogue-of-schurs-tauberian-theorem/B69D4F51393F380CA1ECC5EA584B7A4B

On the enumeration of finite Abelian and solvable groups: On the enumeration of finite Abelian and solvable groups.

Authors: Emre Alkan

Source: Journal of Number Theory. 101:404-423

Subject Terms: Finite abelian groups, Algebra and Number Theory, prime independent multiplicative functions, Prime independent multiplicative function, Local density, Asymptotic results on counting functions for algebraic and topological structures, local density, finite Abelian groups, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0022314X03000556

The Chebotarev theorem for ergodic toral automorphisms with respect to (G, ?)?extensions: The Chebotarev theorem for ergodic toral automorphisms with respect to \((G,\rho)\)-extensions

Authors: Mohd Salmi Md Noorani

Source: Bulletin of the Brazilian Mathematical Society. 34:275-285

Subject Terms: Chebotarev theorem, Fixed points and periodic points of dynamical systems, fixed-point index theory, local dynamics, Functional analytic techniques in dynamical systems, zeta functions, (Ruelle-Frobenius) transfer operators, etc, Lifting theory, Density theorems, Ergodic toral automorphism, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2Fs00574-003-0013-4
https://link.springer.com/content/pdf/10.1007/s00574-003-0013-4.pdf

Asymptotics for logical limit laws: When the growth of the components is in an RT class

Authors: Stanley Burris, Jason P. Bell

Source: Transactions of the American Mathematical Society. 355:3777-3794

Subject Terms: limit law, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Connections of number theory and logic, ratio test, monadic second-order logic, Model theory of finite structures, 0102 computer and information sciences, Schur's Tauberian theorem, Asymptotic enumeration, 01 natural sciences, Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.), Additive number theory, partitions, Generalized primes and integers, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, asymptotic density, zero-one law

File Description: application/xml

Access URL: https://www.ams.org/tran/2003-355-09/S0002-9947-03-03299-9/S0002-9947-03-03299-9.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=644541
https://www.ams.org/tran/2003-355-09/S0002-9947-03-03299-9/S0002-9947-03-03299-9.pdf
https://www.ams.org/journals/tran/2003-355-09/S0002-9947-03-03299-9/home.html

Mean-Value Theorems for Multiplicative Functions on Additive Arithmetic Semigroups via Hal�sz's Method: Mean-value theorems for multiplicative functions on additive arithmetic semigroups via Halász's method

Authors: Wen-Bin Zhang

Source: Monatshefte f�r Mathematik. 138:319-353

Subject Terms: Arithmetic functions in probabilistic number theory, Tauberian theorems, mean-value theorems, Gabor Halász's method, Asymptotic results on arithmetic functions, Asymptotic results on counting functions for algebraic and topological structures, multiplicative functions on additive arithmetic semigroups, existence of mean-values, 0101 mathematics, generating power series, Wirsing's mean-value theorem, 01 natural sciences

File Description: application/xml

Access URL: https://rd.springer.com/content/pdf/10.1007%2Fs00605-002-0503-2.pdf
https://link.springer.com/article/10.1007%2Fs00605-002-0503-2

Closed orbits of (G, τ)‐extension of ergodic toral automorphisms: Closed orbits of \((G,\tau)\)-extension of ergodic toral automorphisms

Authors: Mohd Salmi Md Noorani

Source: International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 17, Pp 1047-1053 (2003)

Subject Terms: asymptotic formula, Fixed points and periodic points of dynamical systems, fixed-point index theory, local dynamics, Functional analytic techniques in dynamical systems, zeta functions, (Ruelle-Frobenius) transfer operators, etc, QA1-939, ergodic automorphism, periodic orbit, closed orbits, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, 01 natural sciences, Mathematics

File Description: application/xml

Access URL: http://downloads.hindawi.com/journals/ijmms/2003/745719.pdf
https://zbmath.org/1930008
https://doi.org/10.1155/s0161171203208164
https://doaj.org/article/d1b36458bf7c48329df1a095f84b56d9
https://downloads.hindawi.com/journals/ijmms/2003/745719.pdf
https://www.hindawi.com/journals/ijmms/2003/745719/
http://downloads.hindawi.com/journals/ijmms/2003/745719.pdf

Frequent Representations: Frequent representations.

Authors: Arnold, Vladimir

Source: Moscow Mathematical Journal. 3:1209-1221

Subject Terms: Ordinary representations and characters, frequent representations, Group actions on varieties or schemes (quotients), Representations of finite groups, frequent representations of finite groups, Representations of finite symmetric groups, Analyse, 01 natural sciences, unitary representations, varieties of representations, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics

File Description: application/xml; application/pdf

Access URL: https://basepub.dauphine.psl.eu/bitstream/123456789/6134/2/2003-17.pdf
https://zbmath.org/2104592

Combinatorial aspects of finitely generated virtually free groups

Authors: Thomas Müller

Source: Groups St Andrews 1989 ISBN: 9780521406697

Subject Terms: Fundamental group, presentations, free differential calculus, asymptotic formula, Generators, relations, and presentations of groups, number of free subgroups of finite index, Free nonabelian groups, finite graph of finite groups, Subgroup theorems, subgroup growth, Asymptotic results on counting functions for algebraic and topological structures, finitely generated virtually free groups, fundamental group

File Description: application/xml

Access URL: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s2-44.1.75

How many elements are needed to generate a finite group with good probability?

Authors: DETOMI, ELOISA MICHELA, LUCCHINI, ANDREA, MORINI F.

Contributors: Detomi, E, Lucchini, A, Morini, Fiorenza, Morini, F

Source: Israel Journal of Mathematics. 132:29-44

Subject Terms: Subgroups of symmetric groups, completely reducible linear groups, Generators, relations, and presentations of groups, Linear algebraic groups over finite fields, permutation groups, randomly chosen elements, Probabilistic methods in group theory, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, 01 natural sciences, numbers of generators, finite groups

File Description: application/xml

Access URL: https://zbmath.org/1874386
https://doi.org/10.1007/bf02784504
https://link.springer.com/article/10.1007%2FBF02784504
https://link.springer.com/content/pdf/10.1007/BF02784504.pdf
https://hdl.handle.net/11577/2461500
https://doi.org/10.1007/BF02784504

On the number of factorizations of an element in an atomic monoid: On the number of factorizations of an element in an atomic monoid.

Authors: José Carlos Rosales, Scott T. Chapman, Pedro A. García-Sánchez, Juan Ignacio García-García

Source: Advances in Applied Mathematics. 29:438-453

Subject Terms: Commutative semigroups, Applied Mathematics, 0102 computer and information sciences, Asymptotic results on counting functions for algebraic and topological structures, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0196885802000258
https://www.sciencedirect.com/science/article/abs/pii/S0196885802000258#!
https://digitalcommons.trinity.edu/math_faculty/82/
https://digitalcommons.trinity.edu/cgi/viewcontent.cgi?article=1083&context=math_faculty
https://hera.ugr.es/doi/15085958.pdf?origin=publication_detail

The expected number of random elements to generate a finite abelian group: The expected number of random elements to generate a finite Abelian group

Authors: Carl Pomerance

Source: Periodica Mathematica Hungarica. 43:191-198

Subject Terms: Finite abelian groups, Generators, relations, and presentations of groups, Probabilistic methods in group theory, 0102 computer and information sciences, Asymptotic results on counting functions for algebraic and topological structures, finite Abelian groups, 0101 mathematics, 01 natural sciences, numbers of generators

File Description: application/xml

Access URL: https://zbmath.org/1668885
https://doi.org/10.1023/a:1015250102792
https://link.springer.com/article/10.1023/A:1015250102792
https://dblp.uni-trier.de/db/journals/pmh/pmh43.html#Pomerance02
http://math.dartmouth.edu/~carlp/PDF/paper123.pdf
https://link.springer.com/content/pdf/10.1023/A:1015250102792.pdf
https://math.dartmouth.edu/~carlp/PDF/paper123.pdf