Modular functions and transcendence questions
From MaRDI portal
Publication:4334999
DOI10.1070/SM1996v187n09ABEH000158zbMath0898.11031OpenAlexW1999172767MaRDI QIDQ4334999
Publication date: 12 June 1997
Published in: Sbornik: Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1070/sm1996v187n09abeh000158
elliptic modular functionEisenstein seriesSchanuel's conjectureelliptic modular formsperiods of elliptic curvesBertrand conjecturealgebraic independence of values of modular forms
Modular and automorphic functions (11F03) Algebraic independence; Gel'fond's method (11J85) Transcendence theory of other special functions (11J91) Holomorphic modular forms of integral weight (11F11) Transcendence theory of elliptic and abelian functions (11J89)
Related Items
The Joint Discrete Universality of Periodic Zeta-Functions ⋮ Quantitative linear independence of an infinite product and its derivatives ⋮ Distribution modulo 1 and universality of the Hurwitz zeta-function ⋮ On joint universality of the Riemann and Hurwitz zeta-functions ⋮ Transcendence of Hurwitz zeta type series and related questions ⋮ MAGNETIC (QUASI-)MODULAR FORMS ⋮ Ramanujan-type identities for Shimura curves ⋮ A criterion of algebraic independence of values of modular functions and an application to infinite products involving Fibonacci and Lucas numbers ⋮ Quantitative irrationality for sums of reciprocals of Fibonacci and Lucas numbers ⋮ TRANSCENDENTAL SUMS RELATED TO THE ZEROS OF ZETA FUNCTIONS ⋮ \(p\)-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions ⋮ On discrete universality of the Hurwitz zeta-function ⋮ Topical problems of the theory of transcendental numbers: development of approaches to their solution in the works of Yu. V. Nesterenko ⋮ On algebraic relations for Ramanujan's functions ⋮ Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers ⋮ A discrete version of the Mishou theorem ⋮ A note on a variant of a conjecture of Rohrlich ⋮ Hermite-Padé rational approximation to irrational numbers ⋮ Algebraic independence of values of quasi-modular forms ⋮ Ramanujan systems of Rankin-Cohen type and hyperbolic triangles ⋮ Multiplicities of Noetherian deformations ⋮ Multiplicity estimate for solutions of extended Ramanujan's system ⋮ On the nature of \(e^{\gamma}\) and non-vanishing of derivatives of \(L\)-series at \(s=1/2\) ⋮ On stable ideals in certain differential rings of Hilbert quasi-modular forms ⋮ Linear independence of certain sums of reciprocals of the Lucas numbers ⋮ An introduction to Mahler's method for transcendence and algebraic independence ⋮ Higher Ramanujan Equations and Periods of Abelian Varieties ⋮ Linear independence of certain numbers in the base-\(b\) number system ⋮ A \(q\)-analogue of the Bailey-Borwein-Bradley identity ⋮ Pfaffian intersections and multiplicity cycles ⋮ On the differential structure of the ring of quasi-modular forms for \(\text{SL}_2(\mathbb Z)\) ⋮ On zeros of quasi-modular forms ⋮ A transcendence theorem in finite characteristic. ⋮ Differential nilradicals of rings associated with Riemann-Schwarz triangular groups ⋮ Algebraic results for certain values of the Jacobi theta-constant $\theta_3(\tau)$ ⋮ Irrationality of certain sums of series. ⋮ Algebraic independence of certain infinite products involving the Fibonacci numbers ⋮ A generalized joint discrete universality theorem for the Riemann and Hurwitz zeta-functions ⋮ A note on special values of 𝐿-functions ⋮ The discrete case of the mixed joint universality for a class of certain partial zeta-functions ⋮ Transformation of generalized multiple Riemann zeta type sums with repeated arguments ⋮ Joint approximation of analytic functions by shifts of the Riemann and periodic Hurwitz zeta-functions ⋮ On irrationality measures of \(\sum^{\infty}_{l=0}d^{l} / \prod^l_{j=1}(1+d^jr+d^{2j}s)\) ⋮ On the algebraic independence of functions of a certain class ⋮ Frequencies of continued fractions and transcendents numbers ⋮ Rational approximations of values of the Gamma function on rationals ⋮ On the largest prime factor of the partition function of \(n\) ⋮ Algebraic relations for reciprocal sums of even terms in Fibonacci numbers ⋮ On the binary expansions of algebraic numbers ⋮ Auxiliary functions in transcendental number theory ⋮ Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers ⋮ A remark on Nesterenko's theorem for Ramanujan functions ⋮ Special values of the gamma function at CM points ⋮ Algebraic independence of certain numbers related to modular functions ⋮ Fontaine's programm ⋮ Linear independence of \(q\)-analogues of certain classical constants ⋮ Mahler and transcendence: effective constructions in transcendental number theory ⋮ Algebraic independence results for the sixteen families of \(q\)-series ⋮ Transcendental values of the digamma function ⋮ Irrationality of \(\zeta _{q}(1)\) and \(\zeta _{q}(2)\) ⋮ On the zeros of weakly holomorphic modular forms ⋮ On the computational complexity of algebraic numbers: the Hartmanis–Stearns problem revisited ⋮ On the irrationality measure for certain series ⋮ A discrete universality theorem for the Hurwitz zeta-function ⋮ Transcendence of power series for some number theoretic functions ⋮ Joint discrete universality for periodic zeta-functions ⋮ Winding of simple walks on the square lattice ⋮ Transcendence and modular functions ⋮ Diophantine properties for 𝑞-analogues of Dirichlet’s beta function at positive integers ⋮ The finiteness of derivation-invariant prime ideals and the algebraic independence of the Eisenstein series ⋮ Transcendence of the log gamma function and some discrete periods ⋮ Elliptic Functions and Transcendence ⋮ Asymptotic representations for Fibonacci reciprocal sums and Euler's formulas for zeta values ⋮ ON LINEAR RELATIONS FOR DIRICHLET SERIES FORMED BY RECURSIVE SEQUENCES OF SECOND ORDER ⋮ Algebraic independence results for values of theta-constants ⋮ A general joint discrete universality theorem for Hurwitz zeta-functions ⋮ Irrationality measures for the series of reciprocals from recurrence sequences. ⋮ Periods of 1-motives and transcendence. ⋮ Infinite series involving hyperbolic functions