Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2019, Volume 371, Issue 2, pp. 1119 - 1149

We give an explicit description of fundamental domains associated with the p-adic uniformisation of families of Shimura curves of discriminant Dp and level N...

Shimura curves | Mumford curves | p-adic fundamental domains | MATHEMATICS | UNIFORMIZATION | CONSTRUCTION | POINTS

Shimura curves | Mumford curves | p-adic fundamental domains | MATHEMATICS | UNIFORMIZATION | CONSTRUCTION | POINTS

Journal Article

2010, Cambridge tracts in mathematics, ISBN 0521197694, Volume 183, xxii, 372

.... On the other hand, the book also provides a thorough introduction to the basics of period domains, as they appear in the geometric approach to local Langlands correspondences and in the...

p-adic fields | Finite fields (Algebra) | Geometry, Algebraic

p-adic fields | Finite fields (Algebra) | Geometry, Algebraic

Book

Journal de l'Ecole Polytechnique - Mathematiques, ISSN 2429-7100, 2017, Volume 4, pp. 37 - 86

Journal Article

2017, Graduate studies in mathematics, ISBN 0821849476, Volume 179., xii, 700 pages

Book

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 09/2013, Volume 49, Issue 3, pp. 413 - 496

We discuss certain arithmetic invariants arising from the monodromy representation in fundamental groups of a family of once punctured elliptic curves of characteristic zero...

Arithmetic fundamental group | Galois representation | Elliptic curve | MATHEMATICS | elliptic curve | PROFINITE BRAID-GROUPS | ALGEBRAS | arithmetic fundamental group | FAMILIES | GROTHENDIECK-TEICHMULLER GROUP | GALOIS REPRESENTATIONS | P-ADIC INTERPOLATION

Arithmetic fundamental group | Galois representation | Elliptic curve | MATHEMATICS | elliptic curve | PROFINITE BRAID-GROUPS | ALGEBRAS | arithmetic fundamental group | FAMILIES | GROTHENDIECK-TEICHMULLER GROUP | GALOIS REPRESENTATIONS | P-ADIC INTERPOLATION

Journal Article

Annales mathématiques du Québec, ISSN 2195-4755, 10/2019, Volume 43, Issue 2, pp. 357 - 409

... domain R that is module-finite over $${\mathcal {O}}[[x_1,\ldots ,x_d]]$$ O [ [ x 1 , … , x d ] ] , where $${\mathcal {O}}$$ O is the ring of integers of a finite extension of the field of p-adic integers...

Two-variable p -adic L -function | Mathematics | 11F67 | 11F33 | 13H10 | Algebra | Nearly ordinary Galois representation | Analysis | Characteristic ideal Euler system | 11F80 | Hida family | Mathematics, general | 11R34 | 11R23 | Number Theory | 13N05 | Two-variable p-adic L-function

Two-variable p -adic L -function | Mathematics | 11F67 | 11F33 | 13H10 | Algebra | Nearly ordinary Galois representation | Analysis | Characteristic ideal Euler system | 11F80 | Hida family | Mathematics, general | 11R34 | 11R23 | Number Theory | 13N05 | Two-variable p-adic L-function

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 06/2016, Volume 1738, Issue 1

In this paper we construct and study the fundamental solution of Cauchy problem for a p-adic parabolic equation where we use pseudodifferential operator on local field defined by Su Weiyi...

pseudodifferential operators | p-adic fields | parabolic equation | Cauchy problems | Markov processes | Cauchy problem

pseudodifferential operators | p-adic fields | parabolic equation | Cauchy problems | Markov processes | Cauchy problem

Conference Proceeding

Bulletin of the American Mathematical Society, ISSN 0273-0979, 10/2019, Volume 56, Issue 4, pp. 611 - 685

Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical...

open problems | FINITE-FIELD PERMUTE | PRIMITIVE DIVISORS | Arithmetic dynamics | DEGREE-GROWTH | WANDERING DOMAINS | PERIODIC POINTS | MATHEMATICS | PREPERIODIC POINTS | QUADRATIC POLYNOMIALS | P-ADIC DYNAMICS | MORDELL-LANG CONJECTURE | RATIONAL MAPS

open problems | FINITE-FIELD PERMUTE | PRIMITIVE DIVISORS | Arithmetic dynamics | DEGREE-GROWTH | WANDERING DOMAINS | PERIODIC POINTS | MATHEMATICS | PREPERIODIC POINTS | QUADRATIC POLYNOMIALS | P-ADIC DYNAMICS | MORDELL-LANG CONJECTURE | RATIONAL MAPS

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 03/2002, Volume 84, Issue 1, pp. 231 - 256

...)$ defined over a non-archimedean field K. We prove that some fundamental conjectures, including the No Wandering Domains conjecture, are equivalent, regardless of which definition of 'component' is used...

p‐adic dynamics | Fatou set | Fatou components | wandering domains | non‐archimedean dynamics | MATHEMATICS | THEOREM | P-ADIC DYNAMICS | CYCLES | SYSTEMS | CANONICAL HEIGHTS | WANDERING DOMAINS

p‐adic dynamics | Fatou set | Fatou components | wandering domains | non‐archimedean dynamics | MATHEMATICS | THEOREM | P-ADIC DYNAMICS | CYCLES | SYSTEMS | CANONICAL HEIGHTS | WANDERING DOMAINS

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 02/2014, Volume 34, Issue 2, pp. 367 - 377

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems < f;...

Ergodic theory | 1-Lipschitz dynamics | 2-adic sphere | P-adic analysis | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | VAN | MAPS | p-adic analysis | THEOREM | LOCAL-FIELDS | ADIC DYNAMICAL-SYSTEMS | Mathematics - Dynamical Systems

Ergodic theory | 1-Lipschitz dynamics | 2-adic sphere | P-adic analysis | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | VAN | MAPS | p-adic analysis | THEOREM | LOCAL-FIELDS | ADIC DYNAMICAL-SYSTEMS | Mathematics - Dynamical Systems

Journal Article

2004, Lecture notes series / Institute for Mathematical Sciences, National University of Singapore, ISBN 9789812387790, Volume 2., x, 415

eBook

2004, Springer monographs in mathematics, ISBN 9780387207117, xi, 390

Book

Progress in physics (Rehoboth, N.M.), ISSN 1555-5534, 04/2006, Volume 2, pp. 46 - 53

By recurring to Geometric Probability methods it is shown that the coupling constants, α^sub EM^, α^sub W^, α^sub C^, associated with the electromagnetic, weak...

Shilov Boundaries | Geometric Probability | p-Adic Hierarchy | Wyler Measure | Coupling Constants

Shilov Boundaries | Geometric Probability | p-Adic Hierarchy | Wyler Measure | Coupling Constants

Journal Article

Algebra and Number Theory, ISSN 1937-0652, 2015, Volume 9, Issue 7, pp. 1571 - 1646

Let f be a primitive Hilbert modular form of parallel weight 2 and level N for the totally real field F, and let p be a rational prime coprime to 2N. If f is...

Hilbert modular forms | Heegner points | Gross–zagier | P-adic heights | P-adic L-functions | ZETA-FUNCTIONS | PERIODS | Birch and Swinnerton-Dyer conjecture | CRITICAL-VALUES | p-adic heights | ARITHMETIC PROPERTIES | MATHEMATICS | Gross-Zagier | ABELIAN-VARIETIES | COHOMOLOGY | p-adic L-functions | CONGRUENCE | DERIVATIVES | Mathematics - Number Theory

Hilbert modular forms | Heegner points | Gross–zagier | P-adic heights | P-adic L-functions | ZETA-FUNCTIONS | PERIODS | Birch and Swinnerton-Dyer conjecture | CRITICAL-VALUES | p-adic heights | ARITHMETIC PROPERTIES | MATHEMATICS | Gross-Zagier | ABELIAN-VARIETIES | COHOMOLOGY | p-adic L-functions | CONGRUENCE | DERIVATIVES | Mathematics - Number Theory

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 12/1997, Volume 124, Issue 4, pp. 309 - 316

LetR be a commutative domain of zero characteristic and letf(X) be a polynomial with coefficients inR...

11S05 | 11R09 | 58F20 | rings of p -adic integers | Mathematics, general | Mathematics | rings of algebraic integers | Polynomial mappings | 58F08 | polynomial orbits | Polynomial orbits | Rings of p-adic integers | Rings of algebraic integers | MATHEMATICS | FIELDS | NUMBER | CYCLES | polynomial mappings | rings of p-adic integers | UNIT EQUATIONS

11S05 | 11R09 | 58F20 | rings of p -adic integers | Mathematics, general | Mathematics | rings of algebraic integers | Polynomial mappings | 58F08 | polynomial orbits | Polynomial orbits | Rings of p-adic integers | Rings of algebraic integers | MATHEMATICS | FIELDS | NUMBER | CYCLES | polynomial mappings | rings of p-adic integers | UNIT EQUATIONS

Journal Article

02/2009, ISBN 9783110207484

eBook

Journal of Number Theory, ISSN 0022-314X, 02/2013, Volume 133, Issue 2, pp. 484 - 491

This paper is devoted to (discrete) p-adic dynamical systems, an important domain of algebraic and arithmetic dynamics...

Measure-preserving | p-Adic numbers | Van der Put basis | Dynamics | Haar measure | P-Adic numbers | SPACE | MATHEMATICS | FIELDS | MAPS | THEOREM

Measure-preserving | p-Adic numbers | Van der Put basis | Dynamics | Haar measure | P-Adic numbers | SPACE | MATHEMATICS | FIELDS | MAPS | THEOREM

Journal Article

Mathematische Annalen, ISSN 0025-5831, 05/2004, Volume 329, Issue 1, pp. 119 - 160

Let K be a number field and A an abelian variety over K. We are interested in the following conjecture of Morita: if the Mumford-Tate group of A does not...

Mathematics, general | Mathematics | MATHEMATICS | MONODROMY | P-ADIC REPRESENTATIONS | DOMAINS | Algebraic Geometry | Number Theory

Mathematics, general | Mathematics | MATHEMATICS | MONODROMY | P-ADIC REPRESENTATIONS | DOMAINS | Algebraic Geometry | Number Theory

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2011, Volume 228, Issue 4, pp. 2116 - 2144

A polynomial of degree ⩾2 with coefficients in the ring of p-adic numbers Z p is studied as a dynamical system on Z p . It is proved that the dynamical...

Quadratic polynomial | p-Adic dynamical system | Minimal component | 37E99 | P-Adic dynamical system | 11S85 | 37A99 | MATHEMATICS | MAPS | RATIONAL FUNCTIONS | CYCLES | LOCAL-FIELDS | NON-ARCHIMEDEAN FIELDS | Dynamical Systems | Mathematics | Number Theory

Quadratic polynomial | p-Adic dynamical system | Minimal component | 37E99 | P-Adic dynamical system | 11S85 | 37A99 | MATHEMATICS | MAPS | RATIONAL FUNCTIONS | CYCLES | LOCAL-FIELDS | NON-ARCHIMEDEAN FIELDS | Dynamical Systems | Mathematics | Number Theory

Journal Article

P-adic numbers, ultrametric analysis, and applications, ISSN 2070-0474, 2010, Volume 2, Issue 1, pp. 77 - 87

.... Thus, the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings...

p-adic mathematical physics | quantum mechanics and field theory | string theory | Mathematics | Algebra

p-adic mathematical physics | quantum mechanics and field theory | string theory | Mathematics | Algebra

Journal Article

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