Search Results - Number theory Algebraic number theory: local and $p$-adic fields*

Number Fields

Authors: Frans Keune

Resource Type: eBook.

Subjects: Algebraic number theory

Categories: MATHEMATICS / Number Theory

Images of Galois representations and p-adic models of Shimura curves

Authors: Amorós Carafí, Laia

Contributors: University/Department: Universitat de Barcelona. Departament d'Àlgebra i Geometria

Thesis Advisors: laiaamca@gmail.com, Bayer i Isant, Pilar, Wiese, Gabor

Source: TDX (Tesis Doctorals en Xarxa)

Subject Terms: Geometria algebraica aritmètica, Geometría algebraica aritmética, Arithmetical algebraic geometry, Àlgebres de Hecke, Álgebras de Hecke, Hecke algebras, Formes modulars, Formas modulares, Modular forms, Camps finits (Àlgebra), Cuerpos modulares (Álgebra), Finite fields (Algebra), Varietats de Shimura, Variedades de Shimura, Shimura varieties, Teoria algebraica de nombres, Teoría algebraica de números, Algebraic number theory, Ciències Experimentals i Matemàtiques

File Description: application/pdf

Access URL: http://hdl.handle.net/10803/471452

A Bibliometric and Topic Modeling Analysis of the p-Adic Theory Literature Using Latent Dirichlet Allocation.

Authors: Llinás, Humberto Gutiérrez, Ismael Torresblanca, Anselmo et al.

Source: Mathematics (2227-7390); Sep2025, Vol. 13 Issue 18, p2932, 18p

Subject Terms: P-adic analysis, NUMBER theory, BIBLIOMETRICS, DOCUMENT clustering, TREND analysis, MATHEMATICAL physics, ALGEBRAIC geometry, CLASSIFICATION

A Formalization of Complete Discrete Valuation Rings and Local Fields

Authors: de Frutos-Fernández, María Inés Nuccio Mortarino Majno di Capriglio, Filippo Alberto Edoardo Universidad Autónoma de Madrid (UAM) et al.

Contributors: de Frutos-Fernández, María Inés Nuccio Mortarino Majno di Capriglio, Filippo Alberto Edoardo Universidad Autónoma de Madrid (UAM) et al.

Source: 13th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP ’24)
https://ujm.hal.science/ujm-04222610
13th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP ’24), Jan 2024, London, United Kingdom. pp.190-204, ⟨10.1145/3636501.3636942⟩
https://popl24.sigplan.org/home/CPP-2024

Subject Terms: Logic and verification, Proof theory formal mathematics, Lean, mathlib, algebraic number theory, local fields, discrete valuation rings, Theory of computation, CCS Concepts: Theory of computation → Logic and verification, Proof theory formal mathematics Lean mathlib algebraic number theory local fields discrete valuation rings, CCS Concepts, Theory of computation → Logic and verification, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]

Subject Geographic: London, United Kingdom

Relation: info:eu-repo/semantics/altIdentifier/arxiv/2310.01998; ARXIV: 2310.01998

Availability: https://ujm.hal.science/ujm-04222610
https://ujm.hal.science/ujm-04222610v3/document
https://ujm.hal.science/ujm-04222610v3/file/deFrutosFerandez%26Nuccio-A%20Formalization%20of%20Complete%20DVR%20and%20Local%20Fields.pdf
https://doi.org/10.1145/3636501.3636942

Some Generalized Fermat-type Equations via Q-Curves and Modularity

Authors: Barroso de Freitas, Nuno Ricardo

Contributors: University/Department: Universitat de Barcelona. Departament d'Algebra i Geometria

Thesis Advisors: nunobfreitas@gmail.com, Dieulefait, L. V. (Luis Victor)

Source: TDX (Tesis Doctorals en Xarxa)

Subject Terms: Equacions, Ecuaciones, Equations, Anàlisi diofàntica, Diophantine analysis, Análisis diofántico, Corbes el·líptiques, Curvas elípticas, Elliptic curves, Geometria algebraica aritmètica, Geometría algebraica aritmética, Arithmetical algebraic geometry, Formes de Hilbert, Formas de Hilbert, Hilbert modular forms, Number Theory, Teoria de nombres, Teoría de números, Ciències Experimentals i Matemàtiques

File Description: application/pdf

Access URL: http://hdl.handle.net/10803/91288

Codes over p-adic Numbers and Finite Rings Invariant under the Full Affine Group: Codes over \(p\)-adic numbers and finite rings invariant under the full affine group

Authors: Kanat Abdukhalikov

Source: Finite Fields and Their Applications. 7:449-467

Subject Terms: Algebra and Number Theory, finite rings, \(p\)-adic numbers, Applied Mathematics, Algebraic coding theory, cryptography (number-theoretic aspects), 02 engineering and technology, 01 natural sciences, affine group, Theoretical Computer Science, affine invariant codes, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Engineering(all), Linear codes (general theory), Algebraic number theory: local fields

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S1071579700902971
https://core.ac.uk/display/82241515
https://www.sciencedirect.com/science/article/abs/pii/S1071579700902971

Algebraic Groups.

Authors: Jakob, Konstantin

Source: Oberwolfach Reports; 2025, Vol. 22 Issue 2, p941-1004, 63p

Subject Terms: LINEAR algebraic groups, ALGEBRAIC geometry, ALGEBRAIC topology, NUMBER theory, REPRESENTATION theory, DIFFERENTIAL equations, ALGEBRAIC combinatorics

A class of spatially inhomogeneous Dirichlet spaces on the p-adic number field: A class of spatially inhomogeneous Dirichlet spaces on the \(p\)-adic number field.

Authors: Hiroshi Kaneko

Source: Stochastic Processes and their Applications. 88:161-174

Subject Terms: Statistics and Probability, Dirichlet forms, recurrence, transience, Applied Mathematics, \(p\)-adic number, 01 natural sciences, inhomogeneous stochastic processes, Harmonic, subharmonic, superharmonic functions on other spaces, Fourier transformation, Recurrence, p-Adic number, Modelling and Simulation, Inhomogeneous stochastic processes, Transience, Jump processes, 0101 mathematics, Diffusion processes, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://zbmath.org/2098327
https://doi.org/10.1016/s0304-4149(99)00124-6
https://www.sciencedirect.com/science/article/abs/pii/S0304414999001246
https://ideas.repec.org/a/eee/spapps/v88y2000i1p161-174.html
https://www.sciencedirect.com/science/article/pii/S0304414999001246
http://directory.umm.ac.id/Data%20Elmu/jurnal/S/Stochastic%20Processes%20And%20Their%20Applications/Vol88.Issue1.2000/925.pdf
https://EconPapers.repec.org/RePEc:eee:spapps:v:88:y:2000:i:1:p:161-174

On the Extension of the von Mises Frequency Approach and Kolmogorov Axiomatic Approach to the p-Adic Probability Theory: On the extensions of the von Mises frequency approach and Kolmogorov axiomatic approach to the \(p\)-adic probability theory

Authors: A. Yu. Khrennikov

Source: Theory of Probability & Its Applications. 40:371-376

Subject Terms: \(p\)-adic numbers, frequency, 0103 physical sciences, \(p\)-adic norm, Foundations of probability theory, 0101 mathematics, 01 natural sciences, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://zbmath.org/850393
https://epubs.siam.org/doi/abs/10.1137/1140040

Attractors of random dynamical systems over p-adic numbers and a model of ‘noisy’ cognitive processes: Attractors of random dynamical systems over \(p\)-adic numbers and a model of ``noisy'' cognitive processes.

Authors: Volker Matthias Gundlach Oliver Steinkamp Daniel Dubischar et al.

Source: Physica D: Nonlinear Phenomena. 130:1-12

Subject Terms: Bifurcation theory for random and stochastic dynamical systems, Cognitive psychology, 0103 physical sciences, 0101 mathematics, 01 natural sciences, Dynamical systems in biology, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://zbmath.org/1370182
https://doi.org/10.1016/s0167-2789(99)00011-1
http://ui.adsabs.harvard.edu/abs/1999PhyD..130....1D/abstract
https://www.sciencedirect.com/science/article/pii/S0167278999000111

The geometric theory of p-adic fields: The geometric theory of \(p\)-adic fields

Authors: Edmund Robinson

Source: Journal of Algebra. 110:158-172

Subject Terms: p-adic fields, Local ground fields in algebraic geometry, p-adically closed fields, Algebra and Number Theory, definable closed sets, General valuation theory for fields, sets of n-th powers, Quantifier elimination, model completeness, and related topics, 01 natural sciences, Non-Archimedean valued fields, quantifier elimination, model completion, 0101 mathematics, Algebraic number theory: local fields, Model theory of fields

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/002186938790041X
https://www.sciencedirect.com/science/article/pii/002186938790041X

Algebraic number fields

Authors: L. V. Kuz'min

Source: Journal of Soviet Mathematics. 38:1930-1988

Subject Terms: arithmetic of abelian fields, Algebraic number theory: global fields, Research exposition (monographs, survey articles) pertaining to number theory, Galois theory, bibliography, algebraic numbers, reference list, 01 natural sciences, Gamma-extensions, p-adic L-functions, survey, local fields, cyclotomic fields, Homological methods (field theory), 0101 mathematics, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2FBF01093434
https://rd.springer.com/article/10.1007/BF01093434

Pair Correlation of Squares in p-Adic Fields: Pair correlation of squares in \(p\)-adic fields.

Authors: Alexandru Zaharescu

Source: Canadian Journal of Mathematics. 55:432-448

Subject Terms: growth conditions, Poisson correlation, Well-distributed sequences and other variations, 0101 mathematics, 01 natural sciences, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://experts.illinois.edu/en/publications/pair-correlation-of-squares-in-p-adic-fields
https://cms.math.ca/10.4153/CJM-2003-019-6

Diophantine Problems Over Local Fields II. A Complete Set of Axioms for p-Adic Number Theory: Diophantine problems over local fields. I. II: A complete set of axioms for \(p\)-adic number theory

Authors: Simon Kochen James Ax

Source: American Journal of Mathematics. 87:631

Subject Terms: Decidability (number-theoretic aspects), \(p\)-adic and power series fields, number theory, Formally \(p\)-adic fields, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://zbmath.org/3221528
https://doi.org/10.2307/2373065
https://www.jstor.org/stable/2373066

K-theory, chamber homology and base change for the p-ADIC groups SL(2), GL(1) and GL(2)

Authors: Aeal, Wemedh Rowley, Peter. Plymen, Roger

Contributors: Aeal, Wemedh Rowley, Peter. Plymen, Roger

Subject Terms: 514.2, K-Theory, Non-Commutative Geometry, Chamber Homology, Base Change, Representation Theory, Number Theory, Algebraic Topology

Access URL: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.554170

ON ERGODIC BEHAVIOR OF p-ADIC DYNAMICAL SYSTEMS: On ergodic behavior of \(p\)-adic dynamical systems

Authors: Mathias Gundlach Karl-Olof Lindahl Andrei Khrennikov

Source: Infinite Dimensional Analysis, Quantum Probability and Related Topics. :569-577

Subject Terms: 37A25, Dynamical Systems (math.DS), Low-dimensional dynamical systems, 37B05, 01 natural sciences, Dynamical systems over complex numbers, FOS: Mathematics, ergodicity, monomial dynamical systems over \(p\)-adic numbers, Relations of ergodic theory with number theory and harmonic analysis, 12J25, Mathematics - Dynamical Systems, 0101 mathematics, Algebraic number theory: local fields

File Description: application/xml

Access URL: http://arxiv.org/pdf/0806.0260
http://arxiv.org/abs/0806.0260
http://www.diva-portal.org/smash/record.jsf?pid=diva2:344785
https://www.worldscientific.com/doi/abs/10.1142/S0219025701000632

Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)

Authors: Zhiyong Zheng Tianze Wang

Resource Type: eBook.

Subjects: Social planning, National security, Number theory

Categories: COMPUTERS / Security / General, MATHEMATICS / Numerical Analysis

A convolutional-like approach to p-adic codes: A convolutional-like approach to \(p\)-adic codes

Authors: N. Lagorce

Source: Discrete Applied Mathematics. 111:139-155

Subject Terms: local field, Applied Mathematics, convolutional code, 0202 electrical engineering, electronic engineering, information engineering, Discrete Mathematics and Combinatorics, Convolutional codes, p-adic codes, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Error correcting codes, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0166218X00003498
https://dblp.uni-trier.de/db/journals/dam/dam111.html#Lagorce01
https://www.sciencedirect.com/science/article/pii/S0166218X00003498

On the birational section conjecture over function fields

Authors: Tyler, Michael Peter Saïdi, Mohamed

Contributors: Tyler, Michael Peter Saïdi, Mohamed

Subject Terms: 510, birational section conjecture, section conjecture, algebraic geometry, arithmetic geometry, diophantine geometry, number theory

Access URL: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739142

On the p-adic Waring's problem: On the \(p\)-adic Waring's problem

Authors: José Felipe Voloch

Source: Acta Arithmetica. 90:91-95

Subject Terms: \(p\)-adic numbers, unramified extension, Waring's problem, Waring's problem and variants, Other analytic theory, 0101 mathematics, 01 natural sciences, Algebraic number theory: local fields

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/110770?download.pdf
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-aav90i1p91bwm
https://eudml.org/doc/207317