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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
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
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
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
Journal Article
by Wu, Bo
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
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
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
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
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
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
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 12/1997, Volume 124, Issue 4, pp. 309 - 316
Journal Article
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
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
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
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
Journal Article
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