Topological transcendence degree. (English) Zbl 1462.14026
MSC:
14G22
Found 3,626 Documents (Results 301–400)
On the linear independence of values of \(G\)-functions. (English) Zbl 1465.11167
Reviewer: Jaroslav Hančl (Ostrava)
On the exceptional set of transcendental functions with integer coefficients in a prescribed set: the problems A and C of Mahler. (English) Zbl 1452.11086
Reviewer: Mahadi Ddamulira (Saarbrücken)
The birthday boy problem. arXiv:2108.06586
Preprint, arXiv:2108.06586 [math.NT] (2021).
Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules. arXiv:2103.09485
Preprint, arXiv:2103.09485 [math.NT] (2021).
Abelian equals A-finite for Anderson A-modules. arXiv:2110.11114
Preprint, arXiv:2110.11114 [math.NT] (2021).
Hyperderivatives of periods and quasi-periods for Anderson \(t\)-modules. arXiv:2103.05836
Preprint, arXiv:2103.05836 [math.NT] (2021).
On the transcendence of special values of Goss \(L\)-functions attached to Drinfeld modules. arXiv:2110.02569
Preprint, arXiv:2110.02569 [math.NT] (2021).
On Wirsing’s problem in small exact degree. arXiv:2108.01484
Preprint, arXiv:2108.01484 [math.NT] (2021).
New Gelfond-Type Transcendental Numbers. arXiv:2106.04055
Preprint, arXiv:2106.04055 [math.NT] (2021).
MSC:
11J81
A note on formal periods. arXiv:2106.03803
Preprint, arXiv:2106.03803 [math.NT] (2021).
Fast-growing series are transcendental. arXiv:2102.12995
Preprint, arXiv:2102.12995 [math.NT] (2021).
Some estimates of the generalized beukers integral with techniques of partial fraction decomposition. arXiv:2101.11396
Preprint, arXiv:2101.11396 [math.NT] (2021).
Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system. (English) Zbl 1513.34358
Arithmetic properties of Euler-type series with a Liouvillian polyadic parameter. (English. Russian original) Zbl 1491.11072
Dokl. Math. 102, No. 2, 412-413 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 494, 68-70 (2020).
Arithmetical results on some infinite products. (English) Zbl 1479.11128
Reviewer: Jaroslav Hančl (Ostrava)
Arithmetic properties of direct product of \(p\)-adic fields elements. (Russian. English summary) Zbl 1471.11213
On transcendental formal power series over finite fields. (English) Zbl 1499.11241
Reviewer: Oto Strauch (Bratislava)
Complex analysis – algebraicity and transcendence. Abstracts from the workshop held August 16–22, 2020 (hybrid meeting). (Komplexe Analysis – algebraicity and transcendence.) (English) Zbl 1469.00027
An equivalence principle between polynomial and simultaneous Diophantine approximation. (English) Zbl 1469.11229
Irrationality exponents of certain fast converging series of rational numbers. (English) Zbl 1481.11072
Reviewer: Marcel G. de Bruin (Heemstede)
The irrationality measure of \(\pi\) as seen through the eyes of \(\cos (n)\). (English) Zbl 1476.11101
MSC:
11J82
Okada’s theorem and multiple Dirichlet series. (English) Zbl 1470.11204
Reviewer: Jaroslav Hančl (Ostrava)
On irrationality measure of some values of \(\arctan \frac{1}{n} \). (English. Russian original) Zbl 1476.11102
Russ. Math. 64, No. 12, 29-37 (2020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 12, 32-40 (2020).
Reviewer: Jaroslav Hančl (Ostrava)
MSC:
11J82
A general theory of André’s solution algebras. (Une théorie générale des algèbres de solutions d’André.) (English. French summary) Zbl 1476.12006
Reviewer: Andreas Maurischat (Aachen)
On the values of hypergeometric functions. (Russian. English summary) Zbl 1464.11072
Reviewer: Jaroslav Hančl (Ostrava)
On linear approximating forms. (Russian. English summary) Zbl 1455.11108
On algebraic identities between solution matrices of generalized hypergeometric equations. (Russian. English summary) Zbl 1464.33005
Reviewer: Štefan Porubský (Praha)
Addendum to “Applications of differential algebra to algebraic independence of arithmetic functions”. (English) Zbl 1454.11134
A note on transcendence over \(p\)-adic fields. (English) Zbl 1459.11151
Reviewer: Jaroslav Hančl (Ostrava)
A new proof of the ultrametric Hermite-Lindermann theorem [A new proof of the ultrametric Hermite-Lindemann theorem]. (English) Zbl 1460.11102
Lectures on the Ax-Schanuel conjecture. (English) Zbl 1452.14007
Nicole, Marc-Hubert (ed.), Arithmetic geometry of logarithmic pairs and hyperbolicity of moduli spaces. Hyperbolicity in Montréal. Based on three workshops, Montréal, Canada, 2018–2019. Cham: Springer. CRM Short Courses, 1-68 (2020).
Some properties of multivariate differential dimension polynomials and their invariants. (English) Zbl 07300087
Mantzaflaris, Angelos (ed.), Proceedings of the 45th international symposium on symbolic and algebraic computation, ISSAC ’20, Kalamata, Greece, July 20–23, 2020. New York, NY: Association for Computing Machinery (ACM). 320-327 (2020).
Degree-one Mahler functions: asymptotics, applications and speculations. (English) Zbl 1461.11109
Reviewer: Tanguy Rivoal (Grenoble)
On approximations of solutions of the equation \(P(z,\ln z) = 0\) by algebraic numbers. (English) Zbl 1456.11128
Reviewer: Jaroslav Hančl (Ostrava)
MSC:
11J82
The irrationality measure of \(\pi\) is at most 7.103205334137…. (English) Zbl 1456.11129
Reviewer: Jaroslav Hančl (Ostrava)
Can polylogarithms at algebraic points be linearly independent? (English) Zbl 1459.11144
Reviewer: István Gaál (Debrecen)
A transference principle for simultaneous rational approximation. (English. French summary) Zbl 1460.11100
Reviewer: Jaroslav Hančl (Ostrava)
Geometric set theory. (English) Zbl 07269808
Mathematical Surveys and Monographs 248. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-5462-3/pbk; 978-1-4704-6018-1/ebook). ix, 330 p. (2020).
The Betti map associated to a section of an abelian scheme. (English) Zbl 1460.11083
Reviewer: Michel Waldschmidt (Paris)
A class of maximally singular sets for rational approximation. (English) Zbl 1455.11097
Reviewer: Jaroslav Hančl (Ostrava)
Some new sums of \(q\)-trigonometric and related functions through a theta product of Jacobi. (English) Zbl 1453.11095
Reviewer: István Mező (Nanjing)
Equivalence of paths in Galilean geometry. (English. Russian original) Zbl 1454.53015
J. Math. Sci., New York 245, No. 3, 297-310 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 144, 3-16 (2018).
Irrationality exponents of generalized Hone series. (English) Zbl 1452.11088
Reviewer: Jaroslav Hančl (Ostrava)
1-\(t\)-motifs. (English) Zbl 1441.11151
Böckle, Gebhard (ed.) et al., \(t\)-motives: Hodge structures, transcendence and other motivic aspects. EMS Series of Congress Reports. Zürich: European Mathematical Society (EMS). 417-439 (2020).
Automata methods in transcendence. (English) Zbl 1441.11052
Böckle, Gebhard (ed.) et al., \(t\)-motives: Hodge structures, transcendence and other motivic aspects. EMS Series of Congress Reports. Zürich: European Mathematical Society (EMS). 351-372 (2020).
An introduction to Mahler’s method for transcendence and algebraic independence. (English) Zbl 1440.11137
Böckle, Gebhard (ed.) et al., \(t\)-motives: Hodge structures, transcendence and other motivic aspects. EMS Series of Congress Reports. Zürich: European Mathematical Society (EMS). 297-349 (2020).
Frobenius difference equations and difference Galois groups. (English) Zbl 1440.11098
Böckle, Gebhard (ed.) et al., \(t\)-motives: Hodge structures, transcendence and other motivic aspects. EMS Series of Congress Reports. Zürich: European Mathematical Society (EMS). 261-295 (2020).
Pink’s theory of Hodge structures and the Hodge conjecture over function fields. (English) Zbl 1451.14013
Böckle, Gebhard (ed.) et al., \(t\)-motives: Hodge structures, transcendence and other motivic aspects. Zürich: European Mathematical Society (EMS). EMS Ser. Congr. Rep., 31-182 (2020).
Generalized Lambert series, Raabe’s cosine transform and a generalization of Ramanujan’s formula for \(\zeta (2m+1)\). (English) Zbl 1462.11064
Reviewer: Khristo N. Boyadzhiev (Ada)
On the irrationality measure of the Thue-Morse constant. (English) Zbl 1451.11080
Reviewer: Mahadi Ddamulira (Saarbrücken)
MSC:
11J82
Diophantine problems and \(p\)-adic period mappings. (English) Zbl 1455.11093
Reviewer: Evis Ieronymou (Nicosia)
Nevanlinna theory and algebraic values of certain meromorphic functions. (English) Zbl 1459.11155
Reviewer: Michel Waldschmidt (Paris)
Simultaneous approximation to values of the exponential function over the adeles. (English) Zbl 1459.11147
Reviewer: István Gaál (Debrecen)
Linear independence of harmonic numbers over the field of algebraic numbers. II. (English) Zbl 1446.11138
Reviewer: Jaroslav Hančl (Ostrava)
On a class of integer-valued functions. (English. Russian original) Zbl 1451.30060
Math. Notes 107, No. 5, 826-837 (2020); translation from Mat. Zametki 107, No. 5, 760-773 (2020).
Reviewer: Michel Waldschmidt (Paris)
On the irrationality measure of \(\ln 7\). (English. Russian original) Zbl 1453.11096
Math. Notes 107, No. 3, 404-412 (2020); translation from Mat. Zametki 107, No. 3, 366-375 (2020).
Reviewer: Jaroslav Hančl (Ostrava)
MSC:
11J82
On the convergence of alternating series associated with Beatty sequences. (English. Russian original) Zbl 1476.11098
Math. Notes 107, No. 2, 345-349 (2020); translation from Mat. Zametki 107, No. 2, 299-303 (2020).
Reviewer: Michael Coons (Callaghan)
Arithmetic properties of generalized hypergeometric \(F\)-series. (English) Zbl 1453.11097
Reviewer: Michael Coons (Callaghan)
\(t\)-motives: Hodge structures, transcendence and other motivic aspects. (English) Zbl 1441.14003
EMS Series of Congress Reports. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-198-9/hbk; 978-3-03719-698-4/ebook). xi, 461 p. (2020).
Linear forms of a given Diophantine type and lattice exponents. (English. Russian original) Zbl 1454.11132
Izv. Math. 84, No. 1, 3-22 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 1, 5-26 (2020).
Reviewer: Jan Šustek (Ostrava)
MSC:
11J82
A short note on generalized Euler-Briggs constants. (English) Zbl 1445.11070
Reviewer: Takao Komatsu (Hangzhou)
MSC:
11J91
Pillars of transcendental number theory. (English) Zbl 1455.11002
Cham: Springer (ISBN 978-981-15-4154-4/hbk; 978-981-15-4155-1/ebook). xvii, 174 p. (2020).
Reviewer: Jaroslav Hančl (Ostrava)
Gelfand-Kirillov dimension for rings. (English) Zbl 1439.16024
Reviewer: Victor Petrogradsky (Brasilia)
Third kind elliptic integrals and 1-motives. (English) Zbl 1450.11077
Reviewer: Mahadi Ddamulira (Saarbrücken)
Hypergeometric rational approximations to \(\zeta (4)\). (English) Zbl 1460.11104
Reviewer: Jaroslav Hančl (Ostrava)
On the computational complexity of algebraic numbers: the Hartmanis-Stearns problem revisited. (English) Zbl 1441.11048
Reviewer: Florian Luca (Johannesburg)
Generalized Lambert series and arithmetic nature of odd zeta values. (English) Zbl 1437.11124
Reviewer: Florian Luca (Johannesburg)
Standard conjectures in model theory, and categoricity of comparison isomorphisms: a model theory perspective. (English) Zbl 1442.14072
Exponents of Diophantine approximation in dimension 2 for numbers of Sturmian type. (English) Zbl 1495.11083
Reviewer: Michel Waldschmidt (Paris)
On exceptional sets of transcendental functions with integer coefficients: solution of a problem of Mahler. (English) Zbl 1450.11078
Reviewer: Mahadi Ddamulira (Saarbrücken)
Linear independence of harmonic numbers over the field of algebraic numbers. (English) Zbl 1441.11180
Reviewer: Jaroslav Hančl (Ostrava)
Linear independence of logarithms of cyclotomic numbers and a conjecture of Livingston. (English) Zbl 1446.11137
Reviewer: Mahadi Ddamulira (Saarbrücken)
Algebraic independence of the values of certain series and their derivatives involving the Hecke-Mahler series. (English) Zbl 1447.11083
Reviewer: John H. Loxton (Greenwich)
Linear relations among asymptotic frequencies in continued fractions. (English) Zbl 1440.11146
Reviewer: Symon Serbenyuk (Kyiv)
Irrationality exponents of numbers related with Cahen’s constant. (English) Zbl 1436.11085
Reviewer: Jaroslav Hančl (Ostrava)
A new exponent of simultaneous rational approximation. (English) Zbl 1462.11056
Reviewer: Jaroslav Hančl (Ostrava)
On transcendental entire functions mapping \(\mathbb{Q}\) into itself. (English) Zbl 1451.11079
Reviewer: Jaroslav Hančl (Ostrava)
Mahler’s method in several variables and finite automata. arXiv:2012.08283
Preprint, arXiv:2012.08283 [math.NT] (2020).
Graded algebras with prescribed Hilbert series. arXiv:2001.01064
Preprint, arXiv:2001.01064 [math.RA] (2020).
Transcendence of zeros of automorphic forms for cuspidal triangle groups. (English. French summary) Zbl 07908817
Simultaneous approximation of values of Jacobi elliptic functions in their real periods. (English) Zbl 07877883
On the mortality problem: from multiplicative matrix equations to linear recurrence sequences and beyond. (English) Zbl 1519.11070
Rossmanith, Peter (ed.) et al., 44th international symposium on mathematical foundations of computer science, MFCS 2019, Aachen, Germany, August 26–30, 2019. Proceedings. Wadern: Schloss Dagstuhl – Leibniz-Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 138, Article 83, 15 p. (2019).
A transference inequality for rational approximation to points in geometric progression. (English) Zbl 1485.11112
Reviewer: Mahadi Ddamulira (Kampala)
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