On the Riemann-Roch theorem on open Riemann surfaces

Shiba, Masakazu

doi:10.1215/kjm/1250523617

Cited by 19 publications

(8 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As we shall see later, for each t E (-1 This lemma was established in [25]. The following lemma is a generalization of the famous bilinear relation due to Legendre and Riemann.…”

Section: T[t {At Bt } Ij [T {At Bt } I] E C(r {A B})mentioning

confidence: 86%

“…The following lemma is a generalization of the famous bilinear relation due to Legendre and Riemann. For the proof, see [25].…”

Section: T[t {At Bt } Ij [T {At Bt } I] E C(r {A B})mentioning

confidence: 99%

“…form a basis (over reals) for the space of holomorphic differentials on R with distinguished real parts (cf. [25]). Therefore there are two real numbers ~,'rJ such that ie--!7rit¢t = ~¢~ + 'rJ¢~.…”

Section: T[t {At Bt } Ij [T {At Bt } I] E C(r {A B})mentioning

confidence: 99%

See 2 more Smart Citations

The moduli of compact continuations of an open Riemann surface of genus one

Shiba¹

1987

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…As we shall see later, for each t E (-1 This lemma was established in [25]. The following lemma is a generalization of the famous bilinear relation due to Legendre and Riemann.…”

Section: T[t {At Bt } Ij [T {At Bt } I] E C(r {A B})mentioning

confidence: 86%

“…The following lemma is a generalization of the famous bilinear relation due to Legendre and Riemann. For the proof, see [25].…”

Section: T[t {At Bt } Ij [T {At Bt } I] E C(r {A B})mentioning

confidence: 99%

See 1 more Smart Citation

The moduli of compact continuations of an open Riemann surface of genus one

Shiba¹

1987

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Shiba [43] proved Theorem 1 in a more general context as an extension of the mapping onto the parallel slit domain. We aim to construct an approximate function of f (z), and all the coefficients of the Laurent expansion (8) as well.…”

Section: Mapping Theorem and The Problemmentioning

confidence: 99%

“…. , θ n arbitrarily assigned to the real axis, respectively [43]. It is a natural generalization of the parallel slit domain, including the following domains listed in Koebe [28]: the horizontal slit domain (θ 1 = · · · = θ n = 0), the horizontal and perpendicular slit domain (θ l = 0 or π/2, l = 1, .…”

Section: Introductionmentioning

confidence: 99%

Numerical conformal mappings onto the linear slit domain

Amano

Okano

Ogata

et al. 2012

Japan J. Indust. Appl. Math.

View full text Add to dashboard Cite

We propose a numerical method for the conformal mapping of unbounded multiply connected domains exterior to closed Jordan curves C 1 , . . . , C n onto a canonical linear slit domain, which is the entire plane with linear slits S 1 , . . . , S n of angles θ 1 , . . . , θ n arbitrarily assigned to the real axis, respectively. If θ 1 = · · · = θ n = θ then it is the well-known parallel slit domain, which is important in the problem of potential flows past obstacles. In the method, we reduce the mapping problem to a boundary value problem for an analytic function, and approximate it by a linear combination of complex logarithmic functions based on the charge simulation method. Numerical examples show the effectiveness of our method.

show abstract

Analytic Continuation beyond the Ideal Boundary

Shiba

2001

Analytic Extension Formulas and Their Applications

View full text Add to dashboard Cite

On the Riemann-Roch theorem on open Riemann surfaces

Cited by 19 publications

References 7 publications

The moduli of compact continuations of an open Riemann surface of genus one

The moduli of compact continuations of an open Riemann surface of genus one

Numerical conformal mappings onto the linear slit domain

Analytic Continuation beyond the Ideal Boundary

Contact Info

Product

Resources

About