Coefficient rings of formal group laws

Buchstaber, Victor Matveevich; Ustinov, A. V.

doi:10.1070/sm2015v206n11abeh004504

Cited by 13 publications

(23 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparing these expressions, we obtain g ′′ (0) = −A 1 , g ′′′ (0) = 2A 2 1 − 2B 2 and expressions (14).…”

Section: From Initial Terms Of the Series Expansion Of Equationmentioning

confidence: 92%

“…Therefore, we assume A 2 = B 1 = 0. For the definition of universal formal group of a given form see [10,14]. The ring of coefficients of the universal formal group of the form (3) is described in [14].…”

Section: Buchstaber Formal Groupmentioning

confidence: 99%

“…Proof. For a formal group (3) with exponential f 4 (x) in relations (14) we have A 1 = 2α, −2B 2 = α 2 − 3β. Substituting these relations into (30) for u = f (x) we obtain the relation…”

Section: Elliptic Function Of Levelmentioning

confidence: 99%

See 2 more Smart Citations

Elliptic function of level 4

Bunkova¹

2016

Proc. Steklov Inst. Math.

View full text Add to dashboard Cite

The work is dedicated to the theory of elliptic functions of level n. An elliptic function of level n determines a Hirzebruch genus that is called elliptic genus of level n. Elliptic functions of level n are also interesting as solutions of Hirzebruch functional equations.The elliptic function of level 2 is the Jacobi elliptic sine. It determines the famous Ochanine-Witten genus. It is the exponential of the universal formal group of the formThe elliptic function of level 3 is the exponential of the universal formal group of the formIn this work we have obtained that the elliptic function of level 4 is the exponential of the universal formal group of the formTo prove this result we have expressed the elliptic function of level 4 in terms of Weierstrass elliptic functions.

show abstract

“…Comparing these expressions, we obtain g ′′ (0) = −A 1 , g ′′′ (0) = 2A 2 1 − 2B 2 and expressions (14).…”

Section: From Initial Terms Of the Series Expansion Of Equationmentioning

confidence: 92%

Section: Buchstaber Formal Groupmentioning

confidence: 99%

See 1 more Smart Citation

Elliptic function of level 4

Bunkova¹

2016

Proc. Steklov Inst. Math.

View full text Add to dashboard Cite

show abstract

“…Therefore either c = 0, and we are in case (1) above, or 5q 4 = −q 2 2 , and we get a series corresponding to the Todd function. 10 10. Classification for n = 5.…”

Section: Todd Functionmentioning

confidence: 99%

Hirzebruch Functional Equation: Classification of Solutions

Bunkova

2018

Proc. Steklov Inst. Math.

View full text Add to dashboard Cite

The Hirzebruch functional equation iswith constant c and initial conditions f (0) = 0, f ′ (0) = 1. In this paper we find all solutions of the Hirzebruch functional equation for n 6 in the class of meromorphic functions and in the class of series. Previously, such results were known only for n 4. The Todd function is the function determining the two-parametric Todd genus (i.e. the χ a,b genus). It gives a solution to the Hirzebruch functional equation for any n. The elliptic function of level N is the function determining the elliptic genus of level N . It gives a solution to the Hirzebruch functional equation for n divisible by N .A series corresponding to a meromorphic function f with parameters in U ⊂ C k is a series with parameters in the Zariski closure of U in C k , such that for parameters in U it coincides with the series expansion at zero of f . The main results are:Theorem. 10.2. Any series solution of the Hirzebruch functional equation for n = 5 corresponds to the Todd function or to the elliptic function of level 5.Theorem. 11.3. Any series solution of the Hirzebruch functional equation for n = 6 corresponds to the Todd function or to the elliptic function of level 2, 3 or 6.This gives a complete classification of complex genera that are fiber multiplicative with respect to CP n−1 for n 6.

show abstract

“…These relations play an important role in describing the coefficient ring of the universal formal group (see [32], [16]) and in the algebraic-topological applications of the formal group in the theory of complex cobordisms (see [36], [43]).…”

Section: Introductionmentioning

confidence: 99%

Analytical and number-theoretical properties of the two-dimensional sigma function

Ayano¹,

Buchstaber²

2020

Preprint

View full text Add to dashboard Cite

This survey is devoted to the classical and modern problems related to the entire function σ(u; λ), defined by a family of nonsingular algebraic curves of genus 2, where u = (u 1 , u 3 ) and λ = (λ 4 , λ 6 , λ 8 , λ 10 ). It is an analogue of the Weierstrass sigma function σ(u; g 2 , g 3 ) of a family of elliptic curves. Logarithmic derivatives of order 2 and higher of the function σ(u; λ) generate fields of hyperelliptic functions of u = (u 1 , u 3 ) on the Jacobians of curves with a fixed parameter vector λ. We consider three Hurwitz series σ(u; λ) = m,n≥0 a m,n (λ)The survey is devoted to the number-theoretic properties of the functions a m,n (λ), ξ k (u 1 ; λ) and µ k (u 3 ; λ). It includes the latest results, which proofs use the fundamental fact that the function σ(u; λ) is determined by the system of four heat equations in a nonholonomic frame of six-dimensional space.

show abstract

Coefficient rings of formal group laws

Cited by 13 publications

References 18 publications

Elliptic function of level 4

Elliptic function of level 4

Hirzebruch Functional Equation: Classification of Solutions

Analytical and number-theoretical properties of the two-dimensional sigma function

Contact Info

Product

Resources

About