المؤلفون: Grosset, M-P., Veselov, A. P.

مصطلحات موضوعية: Mathematics - General Mathematics, Mathematics - Algebraic Geometry, 30B70, 14H40

الوصف: We consider a special class of periodic continued fractions (called alpha-fractions) and discuss the related algebraic and geometric problems. A classical description of the Jacobi variety of a hyperelliptic curve due to Jacobi naturally appears in this context.
Comment: 14 pages

الوصول الحر: http://arxiv.org/abs/math/0701932Test

المؤلفون: Grosset, M. -P., Veselov, A. P.

مصطلحات موضوعية: Mathematical Physics, Mathematics - General Mathematics, 11B68, 81R12

الوصف: A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lam\'e operator.
Comment: Slightly revised version. 14 pages, 1 figure

الوصول الحر: http://arxiv.org/abs/math-ph/0508068Test

المؤلفون: Grosset, M. -P., Veselov, A. P.

مصطلحات موضوعية: Mathematical Physics, Mathematics - General Mathematics, 11B83, 33E05

الوصف: A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is introduced and investigated. This is applied to compute the density of states for the classical Lam\'e operators.
Comment: 22 pages, 1 figure

الوصول الحر: http://arxiv.org/abs/math-ph/0508066Test

المؤلفون: Grosset, M-P., Veselov, A. P.

مصطلحات موضوعية: Mathematics - General Mathematics, Mathematical Physics, 11B68, 37K40

الوصف: We present a new formula for the Bernoulli numbers as the following integral $$B_{2m} =\frac{(-1)^{m-1}}{2^{2m+1}} \int_{-\infty}^{+\infty} (\frac{d^{m-1}}{dx^{m-1}} {sech}^2 x)^2dx. $$ This formula is motivated by the results of Fairlie and Veselov, who discovered the relation of Bernoulli polynomials with soliton theory.
Comment: 5 pages

الوصول الحر: http://arxiv.org/abs/math/0503175Test