Transcendence in Algebra, Combinatorics, Geometry and Number Theory

This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Braov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Brings original articles on algebraic and transcendental aspects of special functions and special numbers Highlights collaboration in number theory, combinatorics, statistical mechanics, and computer algebra Offers selected surveys on key topics in these fields

Inhalt

Frobenius action on a hypergeometric curve and an algorithm for computing values of Dwork's p-adic hypergeometric functions (Asakura).- A Matrix version of Dwork's Congruences (Beukers).- On the kernel curves associated with walks in the quarter plane (Singer).- A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations (Fernandes).- Hodge structures and dierential operators (Vlasenko).- Beck-type identities for Euler pairs of order (Welch et al.).- Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models (Xu et al.).- Infinite product formulae for generating functions for sequences of squares (Radu et al.).- A theta identity of Gauss connecting functions from additive and multiplicative number theory (Merca).- Combinatorial quantum eld theory and the Jacobian conjecture (Tanasa).- How regular are regular singularities? (Hauser).- Néron desingularization of extensions of valuation rings withan appendix by kstutis esnaviius (Popescu).- Diagonal Representation of Algebraic Power Series: A Glimpse Behind the Scenes (Yurkevich).- Proof of chudnovskys' hypergeometric series for 1/ using weber modular polynomials (Guillera).-Computing an order-complete basis for m(n) and applications (Radu et al.).- An algorithm to prove holonomic differential equations for modular forms (Radu et al.).- A case study for (4) (zudilin et al.).- Support of an algebraic series as the range of a recursive sequence (bell).- X-coordinates of pell equations in various sequences (luca).- A conditional proof of the leopoldt conjecture for cm fields (mihailescu).- Siegel's problem for e-functions of order 2 (Roques et al.).- Irrationality and Transcendence of Alternating Series Via Continued Fractions (Snowdow).- On the transcendence of critical hecke l-values (sprang).