Mahler's Measure and Special Values of L-functions

Mahler's Measure and Special Values of L-functions (1998)

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by David W. Boyd

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@MISC{Boyd98mahler'smeasure,
    author = {David W. Boyd},
    title = {Mahler's Measure and Special Values of L-functions},
    year = {1998}
}

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Abstract

this paper is to describe an attempt to understand and generalize a recent formula of Deninger [1997] by means of systematic numerical experiment. This conjectural formula,

Citations

1180	Principles of Algebraic Geometry - Griffiths, Harris - 1978
759	A course in computational algebraic number theory, volume 138 of Graduate Texts in Mathematics - Cohen - 1993
687	The arithmetic of elliptic curves - Silverman - 1985
308	Modular elliptic curves and Fermat’s last theorem - Wiles - 1995
208	Polylogarithms and Associated Functions - Lewin - 1981
197	Ring-theoretic properties of certain Hecke algebras - Taylor, Wiles - 1995
195	Algorithms for modular elliptic curves - Cremona - 1997
93	Numerical Methods for Scientists and Engineers - Hamming - 1986
89	Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 - Cassels, Flynn - 1996
89	Mahler measure and entropy for commuting automorphisms of compact groups - Lind, Schmidt, et al. - 1990
85	Factorization of certain cyclotomic functions - Lehmer - 1933
85	Dynamical systems of Algebraic Origin - Schmidt - 1995
79	curves associated to character varieties of 3–manifolds, Invent - Cooper, Culler, et al. - 1994
69	Valeur de fonctions L et périodes d’intégrales - Deligne
68	Lectures on Elliptic Curves - Cassels - 1991
58	Speculations concerning the range of Mahler’s measure - Boyd - 1981
51	On the product of the conjugates outside the unit circle of an algebraic integer - Smyth - 1971
47	Theory of Algebraic Invariants - Hilbert - 1993
46	On deformation rings and Hecke rings - Diamond - 1996
46	Lessons Introductory to the Modern Higher Algebra - Salmon - 1964
40	Les familles stables de courbes elliptiques sur P1 admettant quarte fibres singulières - Beauville - 1982
40	On measures of polynomials in several variables - Smyth - 1981
39	Deligne Periods of Mixed Motives, K-Theory and the Entropy of Certain Zn-Actions - Deninger - 1997
33	Géométrie D’Arakelov Des Variétés Toriques et Fibrés en Droites Intégrables - Maillot
27	Statistical mechanics of dimers on a plane lattice - Fisher - 1961
24	Polynomials having small measure - Boyd - 1980
22	On some inequalities for polynomials in several variables - Mahler - 1962
21	A problem of Boyd concerning geometric means of polynomials - Lawton - 1983
17	On the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication. In Number theory related to Fermat’s last theorem - Gross - 1981
14	Kronecker’s theorem and Lehmer’s problem for polynomials in several variables - Boyd - 1981
13	K2 and L-functions of elliptic curves: computer calculations. In Applications of Algebraic K-theory to algebraic geometry and number theory, volume 55 - Bloch, Grayson - 1986
13	Two sharp inequalities for the norm of a factor of a polynomial, Mathematika 39 - Boyd - 1992
11	Special values and functional equations of polylogarithms - Zagier - 1991
8	On the Beilinson conjectures for elliptic curves with complex multiplication. In: Beilinson’s conjectures on special values of L-functions. Perspect - Deninger, Wingberg - 1988
8	Height pairings and special values of L-functions - Scholl - 1994
7	Courbes modulaires de genre 1 - Ligozat - 1972
7	Séries de Kronecker et fonctions L des puissances symétriques de courbes elliptiques sur Q - Mestre, Schappacher - 1989
7	Relations between Mahler’s measure and values of L-series - Ray - 1987
7	A Kronecker-type theorem for complex polynomials in several variables - Smyth - 1981
5	L-functions and Tamagawa numbers of motives,The Grothendieck Festschrift - Bloch, Kato - 1990
5	Algorithms for the determination of polynomials with small Mahler measure - Mossinghoff - 1995
4	Spectral behavior of quasiperiodic potentials - Sarnak - 1982
4	Scaling for the discrete Mathieu equation - Thouless
3	Computational Aspects of Curves of Genus at Least 2," Algorithmic Number Theory - Poonen - 1996
3	Ergodic theory of complex continued fractions", pp. 215--226 in Number theory with an emphasis on the Markoff spectrum - Schmidt - 1993
2	The statistics of dimers on a lattice", Physica 27 - Kasteleyn - 1961
2	The metrical theory of complex continued fractions", Acta Arith - Nakada - 1990
2	El'ements explicites dans K 2 d'une courbe elliptique - Rolshausen - 1996
1	User's Guide to Pari-GP 1:39, Universit'e de - Batut, Bernardi, et al. - 1995
1	Higher regulators and values of L-functions of curves", Funktsional. Anal. i Prilozhen - Beilinson - 1980