Mahler functions and transcendence
From MaRDI portal
Publication:1922724
DOI10.1007/BFb0093672zbMath0876.11034MaRDI QIDQ1922724
Publication date: 23 September 1996
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
functional equationtranscendencealgebraic independenceregular sequencesMahler's methodMahler functionsNesterenko's methodMasser's vanishing theorem
Research exposition (monographs, survey articles) pertaining to number theory (11-02) Algebraic independence; Gel'fond's method (11J85) Special sequences and polynomials (11B83) Transcendence (general theory) (11J81) Automata sequences (11B85)
Related Items
Algebraic independence results for a certain family of power series, infinite products, and Lambert type series ⋮ A height gap theorem for coefficients of Mahler functions ⋮ Frobenius method for Mahler equations ⋮ Guided by Schwarz’ Functions: A Walk Through the Garden of Mahler’s Transcendence Method ⋮ On formal inverse of the Prouhet-Thue-Morse sequence ⋮ On some arithmetic properties of Mahler functions ⋮ Graded algebras, algebraic functions, planar trees, and elliptic integrals ⋮ A criterion for linear independence of series ⋮ On the convergence of Diophantine Dirichlet series ⋮ Transcendence of reciprocal sums of binary recurrences ⋮ Walks confined in a quadrant are not always D-finite ⋮ Spectral theory of regular sequences ⋮ VARIATIONS AROUND A PROBLEM OF MAHLER AND MENDÈS FRANCE ⋮ Computing solutions of linear Mahler equations ⋮ Groupes de Galois et nombres automatiques ⋮ Polynomial dynamics and local analysis of small and grand orbits ⋮ THE TRANSCENDENCE OF SERIES RELATED TO STERN'S DIATOMIC SEQUENCE ⋮ Unnamed Item ⋮ Algebraic independence of certain entire functions of two variables generated by linear recurrences ⋮ Transcendence of the values of infinite products in several variables ⋮ On algebraic independence of a class of infinite products ⋮ Algebraic independence of certain Mahler functions ⋮ Differential transcendence of solutions of the difference equation \(\Delta y=ay^2 +by+c\) ⋮ Transcendence of certain series involving binary linear recurrences ⋮ Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion ⋮ Entire functions with undecidable arithmetic properties ⋮ A Fibonacci type sequence with Prouhet–Thue–Morse coefficients ⋮ Calibrating generative models: the probabilistic Chomsky-Schützenberger hierarchy ⋮ Algebraic theory of difference equations and Mahler functions ⋮ Hypertranscendence and algebraic independence of certain infinite products ⋮ Topical problems of the theory of transcendental numbers: development of approaches to their solution in the works of Yu. V. Nesterenko ⋮ Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field ⋮ Transcendence of certain infinite products ⋮ Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL ⋮ On the algebraic relations between Mahler functions ⋮ TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF SERIES RELATED TO STERN'S SEQUENCE ⋮ Algebraic independence of the partial derivatives of certain functions with arbitrary number of variables ⋮ An algorithm to recognize regular singular Mahler systems ⋮ Some product formulas ⋮ Transcendence of polynomial canonical heights ⋮ Algebraic and arithmetical properties of Mahler infinite products generated by the second degree polynomials ⋮ An arithmetical property of the real numbers generated by Thue-Morse sequence along squares ⋮ Irrationality of infinite series ⋮ Algebraic independence of the values of power series and their derivatives generated by linear recurrences ⋮ Asymptotic distance and its application ⋮ (Non)Automaticity of number theoretic functions ⋮ An introduction to Mahler's method for transcendence and algebraic independence ⋮ On the irrationality measure of the Thue–Morse constant ⋮ \(p\)-adic transcendence and \(p\)-adic transcendence measures for the values of Mahler type functions ⋮ Méthode de Mahler en caractéristique non nulle : un analogue du théorème de Ku. Nishioka ⋮ Algebraic independence of the generating functions of Stern's sequence and of its twist ⋮ Note on the Stern-Brocot sequence, some relatives, and their generating power series ⋮ ON THE TRANSCENDENCE OF CERTAIN REAL NUMBERS ⋮ Algebraic independence results for the values of certain Mahler functions and their application to infinite products ⋮ Multiplicative analogue of Markoff-Lagrange spectrum and Pisot numbers ⋮ On expressible sets of products ⋮ ON THE BITS COUNTING FUNCTION OF REAL NUMBERS ⋮ Unnamed Item ⋮ Algebraic independence of the generating functions of the stern polynomials and their twisted analogues ⋮ Arithmetical results on some infinite products ⋮ Criteria for regularity of Mahler power series and Becker's conjecture ⋮ Unnamed Item ⋮ Algebraic independence of reciprocal sums of powers of certain Fibonacci-type numbers ⋮ Diophantine approximation ⋮ Algebraic independence over \(\mathbb Q_p\) ⋮ Algebraic independence results related to pattern sequences in distinct \(\langle q,r \rangle\)-numeration systems ⋮ Transcendence criterion for values of certain functions of several variables ⋮ Auxiliary functions in transcendental number theory ⋮ Unnamed Item ⋮ New results on algebraic independence with Mahler's method ⋮ Algebraic independence of local conjugacies and related questions in polynomial dynamics ⋮ Linearly unrelated sequences and problem of Erdős ⋮ Algebraic independence of power series generated by linearly independent positive numbers ⋮ Pattern sequences in \(\langle q,r\rangle\)-numeration systems ⋮ Algebraic independence of the values of the Hecke–Mahler series and its derivatives at algebraic numbers ⋮ Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series ⋮ Mahler's classification of complex numbers ⋮ Rotation number of contracted rotations ⋮ On \(p\)-adic valuations of certain \(m\) colored \(p\)-ary partition functions ⋮ Algebraic independence of the values of certain series and their derivatives involving the Hecke-Mahler series ⋮ Arithmetic properties of solutions of certain functional equations with transformations represented by matrices including a negative entry ⋮ ARITHMETIC PROPERTIES OF INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS ⋮ Transcendence and modular functions ⋮ \(q\)-linear functions and algebraic independence. ⋮ Becker’s conjecture on Mahler functions ⋮ Conditions for the algebraic independence of certain series involving continued fractions and generated by linear recurrences ⋮ Life and Mathematics of Alfred Jacobus van der Poorten (1942–2010) ⋮ AN ARITHMETICAL EXCURSION VIA STONEHAM NUMBERS ⋮ Regular extensions and algebraic relations between values of Mahler functions in positive characteristic ⋮ On arithmetic properties of binary partition polynomials ⋮ The transcendence of certain infinite series ⋮ Transcendental series of reciprocals of Fibonacci and Lucas numbers ⋮ On rational approximations of certain Mahler functions with a connection to the Thue–Morse sequence ⋮ Irrational rapidly convergent series ⋮ Diophantine approximation of Mahler numbers ⋮ ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES ⋮ A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations ⋮ Algebraic independence of the power series defined by blocks of digits ⋮ On certain Mahler functions ⋮ Arithmetical properties of certain infinite products ⋮ On the beta-expansions of 1 and algebraic numbers for a Salem number beta ⋮ Irrationality measures for the series of reciprocals from recurrence sequences.
