LEADER 05279nam 22008055 450 001 9910508453303321 005 20251230055107.0 010 $a3-030-84304-1 024 7 $a10.1007/978-3-030-84304-5 035 $a(CKB)4940000000616355 035 $a(MiAaPQ)EBC6797893 035 $a(Au-PeEL)EBL6797893 035 $a(OCoLC)1283859068 035 $a(PPN)258840781 035 $a(BIP)82074652 035 $a(BIP)80849855 035 $a(DE-He213)978-3-030-84304-5 035 $a(EXLCZ)994940000000616355 100 $a20211102d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTranscendence in Algebra, Combinatorics, Geometry and Number Theory $eTRANS19 ? Transient Transcendence in Transylvania, Bra?ov, Romania, May 13?17, 2019, Revised and Extended Contributions /$fedited by Alin Bostan, Kilian Raschel 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (544 pages) $cillustrations 225 1 $aSpringer Proceedings in Mathematics & Statistics,$x2194-1017 ;$v373 311 08$a3-030-84303-3 320 $aIncludes bibliographical references. 327 $aFrobenius 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 di?erential 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 k?stutis ?esnavi?ius (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). 330 $aThis proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Bra?ov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees. 410 0$aSpringer Proceedings in Mathematics & Statistics,$x2194-1017 ;$v373 606 $aFunctions, Special 606 $aNumber theory 606 $aProbabilities 606 $aDiscrete mathematics 606 $aCommutative algebra 606 $aCommutative rings 606 $aMathematical physics 606 $aSpecial Functions 606 $aNumber Theory 606 $aProbability Theory 606 $aDiscrete Mathematics 606 $aCommutative Rings and Algebras 606 $aTheoretical, Mathematical and Computational Physics 615 0$aFunctions, Special. 615 0$aNumber theory. 615 0$aProbabilities. 615 0$aDiscrete mathematics. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aMathematical physics. 615 14$aSpecial Functions. 615 24$aNumber Theory. 615 24$aProbability Theory. 615 24$aDiscrete Mathematics. 615 24$aCommutative Rings and Algebras. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a515.22 702 $aRaschel$b Kilian 702 $aBostan$b Alin 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910508453303321 996 $aTranscendence in Algebra, Combinatorics, Geometry and Number Theory$92568907 997 $aUNINA