The Prime Geodesic Theorem in Arithmetic Progressions: The prime geodesic theorem in arithmetic progressions

Authors: Chatzakos, Dimitrios, Harcos, Gergely, Kaneko, Ikuya

Source: International Mathematics Research Notices. 2024:13180-13190

Subject Terms: arithmetic progression, prime geodesic theorem, Mathematics - Number Theory, Analytic theory (Epstein zeta functions, relations with automorphic forms and functions), Arithmetic progressions, \(\zeta (s)\) and \(L(s, \chi)\), FOS: Mathematics, Structure of modular groups and generalizations, arithmetic groups, Number Theory (math.NT), 11F72 (primary), 11M36 (secondary)

File Description: application/xml

Access URL: http://arxiv.org/abs/2309.04186

Geometry and arithmetic of semi‐arithmetic Fuchsian groups: Geometry and arithmetic of semi-arithmetic Fuchsian groups

Authors: Mikhail Belolipetsky, Gregory Cosac, Cayo Dória, Gisele Teixeira Paula

Source: Journal of the London Mathematical Society. 111

Subject Terms: Mathematics - Geometric Topology, Mathematics - Metric Geometry, Mathematics - Number Theory, 20H10, 11F06, 30F10, FOS: Mathematics, Compact Riemann surfaces and uniformization, Structure of modular groups and generalizations, arithmetic groups, Geometric Topology (math.GT), Metric Geometry (math.MG), Group Theory (math.GR), Number Theory (math.NT), Fuchsian groups and their generalizations (group-theoretic aspects), Mathematics - Group Theory

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Access URL: http://arxiv.org/abs/2310.13151

A dominance semigroup of the modular group

Authors: Hardy, Darel, Wisner, Robert J.

Source: Publicationes Mathematicae Debrecen. 19:145-149

Subject Terms: Structure of modular groups and generalizations, arithmetic groups, 0101 mathematics, Matrices, determinants in number theory, Matrices of integers, 01 natural sciences

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Access URL: https://zbmath.org/3424113

Algebraic curves uniformized by congruence subgroups of triangle groups

Authors: Pete L. Clark, John Voight

Source: Transactions of the American Mathematical Society. 371:33-82

Subject Terms: weak rigidity, fields of definition, Mathematics - Number Theory, Arithmetic aspects of dessins d'enfants, Belyĭ theory, congruence subgroups, FOS: Mathematics, Structure of modular groups and generalizations, arithmetic groups, triangle groups, Number Theory (math.NT), 0101 mathematics, Galois Belyĭ maps, 01 natural sciences, Modular and Shimura varieties

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Access URL: http://arxiv.org/abs/1506.01371
https://zbmath.org/6993226
https://doi.org/10.1090/tran/7139
https://ui.adsabs.harvard.edu/abs/2015arXiv150601371C/abstract
https://math.dartmouth.edu/~jvoight/articles/triangle-072011.pdf
http://math.uga.edu/~pete/triangle-091309.pdf
http://math.dartmouth.edu/~jvoight/articles/triangle-072011.pdf
http://alpha.math.uga.edu/~pete/triangle-012116.pdf
https://www.ams.org/tran/earlyview/#tran7139

Seventy years of Salem numbers

Authors: Chris Smyth

Source: Bulletin of the London Mathematical Society. 47:379-395

Subject Terms: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc, Convolution, factorization for one variable harmonic analysis, Mathematics - Number Theory, Fuchsian groups, Structure of modular groups and generalizations, arithmetic groups, Coxeter groups, 01 natural sciences, Salem numbers, \(K3\) surfaces, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Reflection and Coxeter groups (group-theoretic aspects), FOS: Mathematics, 11R06, \(K3\) surfaces and Enriques surfaces, Knots and links in the \(3\)-sphere, Number Theory (math.NT), Bernoulli convolutions, Alexander polynomials, 0101 mathematics, Fuchsian groups and their generalizations (group-theoretic aspects)

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Access URL: http://arxiv.org/pdf/1408.0195
http://arxiv.org/abs/1408.0195
http://www.maths.ed.ac.uk/~chris/papers/Salem_survey220315.pdf
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms/bdv027
https://www.maths.ed.ac.uk/~chris/papers/Salem_survey220315.pdf
https://arxiv.org/abs/1408.0195
https://arxiv.org/pdf/1408.0195.pdf
http://ui.adsabs.harvard.edu/abs/2014arXiv1408.0195S/abstract

On Non-Congruence Subgroups of the Analogue of the Modular Group in Characteristic p: On non-congruence subgroups of the analogue of the modular group in characteristic \(p\).

Authors: A. W. Mason

Source: Developments in Mathematics ISBN: 9781441953957

Subject Terms: Unimodular groups, congruence subgroups (group-theoretic aspects), congruece subgroups, polynomial rings, non-congruence subgroups, Structure of modular groups and generalizations, arithmetic groups, Fuchsian groups and their generalizations (group-theoretic aspects), special linear groups, minimal index

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Access URL: http://eprints.gla.ac.uk/12938/
https://link.springer.com/chapter/10.1007/978-1-4757-6044-6_11
https://rd.springer.com/chapter/10.1007/978-1-4757-6044-6_11

On the Extended Hecke Group $\overline{H}(\lambda_5)$: On the extended Hecke group \(\overline H(\lambda_5)\).

Authors: Sebahattin Ikikardes, Özden Koruoğlu, Recep Sahin

Source: Algebra Colloquium. 13:17-23

Subject Terms: commutator subgroup, power subgroups, Structure of modular groups and generalizations, arithmetic groups, extended Hecke groups, 0101 mathematics, Fuchsian groups and their generalizations (group-theoretic aspects), 01 natural sciences

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Access URL: https://zbmath.org/2243323
https://doi.org/10.1142/s1005386706000046
https://www.worldscientific.com/doi/10.1142/S1005386706000046

Generations for Arithmetic Groups: Generations for arithmetic groups.

Authors: T. N. Venkataramana, R. Sharma

Source: Geometriae Dedicata. 114:103-146

Subject Terms: Generators, relations, and presentations of groups, Unimodular groups, congruence subgroups (group-theoretic aspects), Subgroup theorems, subgroup growth, Structure of modular groups and generalizations, arithmetic groups, higher rank real semi-simple Lie groups, Discrete subgroups of Lie groups, 01 natural sciences, subgroups of finite index, 0103 physical sciences, higher rank arithmetic groups, congruence subgroups, 0101 mathematics, irreducible lattices, generators

File Description: application/xml

Access URL: https://zbmath.org/2227560
https://doi.org/10.1007/s10711-005-0123-9
https://link.springer.com/article/10.1007/s10711-005-0123-9

Trace coordinates of Teichmüller space of Riemann surfaces of signature (0,4): Trace coordinates of Teichmüller space of Riemann surfaces of signature \((0,4)\)

Authors: Klaus-Dieter Semmler, Thomas Gauglhofer

Source: Conformal Geometry and Dynamics of the American Mathematical Society. 9:46-75

Subject Terms: Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Structure of modular groups and generalizations, arithmetic groups, 0101 mathematics, Teichmüller theory for Riemann surfaces, 01 natural sciences

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Access URL: https://www.ams.org/ecgd/2005-09-03/S1088-4173-05-00106-2/S1088-4173-05-00106-2.pdf
http://ui.adsabs.harvard.edu/abs/2005CGDAM...9...46G/abstract
https://www.ams.org/ecgd/2005-09-03/S1088-4173-05-00106-2/S1088-4173-05-00106-2.pdf
https://www.ams.org/journals/ecgd/2005-09-03/S1088-4173-05-00106-2/home.html
https://infoscience.epfl.ch/record/161446

PROOF OF A CONJECTURE RELATED TO THE PARABOLIC CLASS NUMBERS OF SOME FUCHSIAN GROUPS: Proof of a conjecture related to the parabolic class numbers of some Fuchsian groups.

Authors: Özgür, Nihal Yılmaz, Keskin, Refik

Contributors: Fen Edebiyat Fakültesi, orcid:0000-0002-8152-1830

Source: Acta Mathematica Scientia. 25:215-222

Subject Terms: Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), normalizers, Unimodular groups, congruence subgroups (group-theoretic aspects), Fuchsian Group, Discrete Group, parabolic class numbers, Fuchsian groups, Structure of modular groups and generalizations, arithmetic groups, Parabolic Class Number, 0101 mathematics, Fuchsian groups and their generalizations (group-theoretic aspects), Hecke groups, 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/2199115
https://doi.org/10.1016/s0252-9602(17)30278-3
http://dspace.balikesir.edu.tr/handle/20.500.12462/7824
https://www.sciencedirect.com/science/article/pii/S0252960217302783

THE MINIMUM INDEX OF A NON-CONGRUENCE SUBGROUP OF SL2 OVER AN ARITHMETIC DOMAIN. II: THE RANK ZERO CASES: The minimum index of a non-congruence subgroup of \(\text{SL}_2\) over an arithmetic domain. II: The rank zero cases.

Authors: A. W. Mason, Andreas Schweizer

Source: Journal of the London Mathematical Society. 71:53-68

Subject Terms: Unimodular groups, congruence subgroups (group-theoretic aspects), Congruence subgroup problems, subgroups of finite index, non-congruence subgroups, 0103 physical sciences, Subgroup theorems, subgroup growth, Structure of modular groups and generalizations, arithmetic groups, arithmetic Dedekind domains, 0101 mathematics, 01 natural sciences, Linear algebraic groups over global fields and their integers

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Access URL: https://zbmath.org/2162718
https://doi.org/10.1112/s0024610704006027
http://doi.wiley.com/10.1112/S0024610704006027
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024610704006027
http://eprints.gla.ac.uk/12923/
https://www.cambridge.org/core/journals/journal-of-the-london-mathematical-society/article/minimum-index-of-a-noncongruence-subgroup-of-sl2-over-an-arithmetic-domain-ii-the-rank-zero-cases/F4E9B099336789FDB4BB6431477BDE61
https://academic.oup.com/jlms/article/71/1/53/932672
https://documat.unirioja.es/servlet/articulo?codigo=2206235

The congruence subgroup problem: The congruence subgroup problem.

Authors: M. S. Raghunathan

Source: Proceedings Mathematical Sciences. 114:299-308

Subject Terms: Unimodular groups, congruence subgroups (group-theoretic aspects), 0103 physical sciences, congruence subgroups, FOS: Mathematics, Structure of modular groups and generalizations, arithmetic groups, Group Theory (math.GR), integral unimodular groups, 0101 mathematics, Mathematics - Group Theory, 01 natural sciences

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Access URL: http://arxiv.org/pdf/math/0503088v1.pdf
http://arxiv.org/abs/math/0503088
https://zbmath.org/2139579
https://doi.org/10.1007/bf02829437
https://arxiv.org/pdf/math/0503088
https://ui.adsabs.harvard.edu/abs/2005math......3088R/abstract
https://www.mathi.uni-heidelberg.de/~wienhard/retreat10/references/raghunathan_csp.pdf
http://www.mathi.uni-heidelberg.de/~wienhard/retreat10/references/raghunathan_csp.pdf
https://link.springer.com/article/10.1007/BF02829437
https://www.arxiv-vanity.com/papers/math/0503088/

On Rademacher's conjecture: congruence subgroups of genus zero of the modular group: On Rademacher's conjecture: congruence subgroups of genus zero of the modular group.

Authors: Chua, K.S., Lang, M.L., Yang, Y.

Contributors: MATHEMATICS

Source: Journal of Algebra. 277:408-428

Subject Terms: Unimodular groups, congruence subgroups (group-theoretic aspects), Algebra and Number Theory, Genus, numbers of cusps, Modular group, Subgroup theorems, subgroup growth, modular group, Structure of modular groups and generalizations, arithmetic groups, function fields, 01 natural sciences, genera, Rademacher conjecture, fundamental polygons, congruence subgroups, Hauptmodul, indices, Farey symbols, 0101 mathematics, Congruence subgroups, generators

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Access URL: https://www.sciencedirect.com/science/article/pii/S0021869304001395
https://core.ac.uk/display/82119363
https://ir.nctu.edu.tw:443/handle/11536/26611
http://www.sciencedirect.com/science/article/pii/S0021869304001395

On extension of the modular transformations over the modular group by reflection: On extension of the modular transformations over the modular group by reflection.

Authors: Yildiz, I

Contributors: Ondokuz Mayıs Üniversitesi

Source: Applied Mathematics and Computation. 153:111-116

Subject Terms: Generators, relations, and presentations of groups, Unimodular groups, congruence subgroups (group-theoretic aspects), 0103 physical sciences, modular transformations, congruence subgroups, modular group, Structure of modular groups and generalizations, arithmetic groups, 0101 mathematics, Fuchsian groups and their generalizations (group-theoretic aspects), generators, 01 natural sciences

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/amc/amc153.html#Yildiz04
https://www.sciencedirect.com/science/article/abs/pii/S0096300303006143
http://www.sciencedirect.com/science/article/pii/S0096300303006143

The large scale topology and algebraic K-theory of arithmetic groups: The large scale topology and algebraic \(K\)-theory of arithmetic groups

Authors: Boris Goldfarb

Source: Topology and its Applications. 140:267-294

Subject Terms: Arithmetic group, Assembly map, compact singular variety, Structure of modular groups and generalizations, arithmetic groups, \(K\)-theory, Discrete subgroups of Lie groups, Symmetric space, K-theory, 01 natural sciences, Chern character, Extensions of spaces (compactifications, supercompactifications, completions, etc.), 0103 physical sciences, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Geometry and Topology, 0101 mathematics, Geometric group theory, Differential geometry of symmetric spaces

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Access URL: https://zbmath.org/2105282
https://doi.org/10.1016/j.topol.2003.07.012
https://www.sciencedirect.com/science/article/pii/S0166864103002955#!
https://core.ac.uk/display/82702012
https://www.sciencedirect.com/science/article/pii/S0166864103002955
https://www.sciencedirect.com/science/article/abs/pii/S0166864103002955
http://math.albany.edu:8000/~goldfarb/papers_html/arithmetic.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

The minimum index of a non-congruence subgroup of SL2 over an arithmetic domain: The minimum index of a non-congruence subgroup of \(\text{SL}_2\) over an arithmetic domain

Authors: A. W. Mason, Andreas Schweizer

Source: Israel Journal of Mathematics. 133:29-44

Subject Terms: Unimodular groups, congruence subgroups (group-theoretic aspects), subgroups of finite index, non-congruence subgroups, arithmetic Dedekind rings, Subgroup theorems, subgroup growth, Structure of modular groups and generalizations, arithmetic groups, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1910261
https://doi.org/10.1007/bf02773059
http://eprints.gla.ac.uk/12921/
https://link.springer.com/content/pdf/10.1007/BF02773059.pdf
https://link.springer.com/article/10.1007/BF02773059

The modular automorphisms of the Drinfeld modular curve $$ X_{1}(\frak n) $$: The modular automorphisms of the Drinfeld modular curve \(X_1(\mathfrak n)\)

Authors: M. Tripolitaki

Source: Archiv der Mathematik. 81:524-533

Subject Terms: Drinfeld modular curve, modular automorphisms, Modular forms associated to Drinfel'd modules, Structure of modular groups and generalizations, arithmetic groups, Drinfel'd modules, higher-dimensional motives, etc, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s00013-003-4751-8
https://rd.springer.com/article/10.1007/s00013-003-4751-8

Hecke Groups, Polynomial Maps and Matings: Hecke groups, polynomial maps and matings

Authors: Shaun Bullett, Marianne Freiberger

Source: International Journal of Modern Physics B. 17:3922-3931

Subject Terms: Structure of modular groups and generalizations, arithmetic groups, 0101 mathematics, Fuchsian groups and their generalizations (group-theoretic aspects), 01 natural sciences, Dynamical systems involving relations and correspondences in one complex variable

File Description: application/xml

Access URL: https://zbmath.org/2200421
https://doi.org/10.1142/s0217979203021915
http://ui.adsabs.harvard.edu/abs/2003IJMPB..17.3922B/abstract

The connection between quadratic forms and the extended modular group: The connection between quadratic forms and the extended modular group.

Authors: Tekcan, Ahmet, Bizim, Osman

Source: Mathematica Bohemica. 128:225-236

Subject Terms: extended modular group, 4. Education, binary quadratic forms, Structure of modular groups and generalizations, arithmetic groups, reduced forms, 0101 mathematics, Sums of squares and representations by other particular quadratic forms, 01 natural sciences

File Description: application/xml

Access URL: http://dml.cz/bitstream/handle/10338.dmlcz/134178/MathBohem_128-2003-3_1.pdf
https://avesis.uludag.edu.tr/yayin/dc4e0053-0369-4dbd-adb8-b772345c1b52/the-connection-between-quadratic-forms-and-the-extended-modular-group
https://dml.cz/handle/10338.dmlcz/134178
https://avesis.uludag.edu.tr/publication/details/dc4e0053-0369-4dbd-adb8-b772345c1b52/oai