Periods of hyperelliptic integrals expressed in terms of θ -constants by means of Thomae formulae

DOI10.1098/rsta.2007.2059zbMath1153.33308OpenAlexW2117515263WikidataQ51911749 ScholiaQ51911749MaRDI QIDQ5503947

Peter H. Richter, Viktor Z.Enol'skij

Publication date: 21 January 2009

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rsta.2007.2059

zbMATH Keywords

Picard-Fuchs equations\(\theta \)-constantsRiemann \(\theta \)-functions

Mathematics Subject Classification ID

Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Elliptic functions and integrals (33E05)

Related Items (17)

Hyperelliptic theta-functions and spectral methods ⋮ Sets of special subvarieties of bounded degree ⋮ New generalisation of Jacobi's derivative formula ⋮ Decomposing Jacobians Via Galois covers ⋮ Genus two Siegel quasi-modular forms and Gromov-Witten theory of toric Calabi-Yau threefolds ⋮ On a formula of spin sums, Eisenstein-Kronecker series in higher genus Riemann surfaces ⋮ The mean values of the Weierstrass elliptic function \(\wp\): theory and application ⋮ General derivative Thomae formula for singular half-periods ⋮ Thomae type formulae for singular \(Z_N\) curves ⋮ Finite Unions of Intervals, Part I ⋮ The Picard–Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system ⋮ Image of Abel-Jacobi map for hyperelliptic genus 3 and 4 curves ⋮ Computational approach to hyperelliptic Riemann surfaces ⋮ Non-perturbative studies of N=2 conformal quiver gauge theories ⋮ Thomae's derivative formulae for trigonal curves ⋮ Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models ⋮ Rosenhain-Thomae formulae for higher genera hyperelliptic curves

Cites Work

• On the smoothed finite element method (Int. J. Numer. Meth. Engng2008;76:1285-1295 (DOI: 10.1002/nme.2460))

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