By Gisbert Wüstholz
Alan Baker's sixtieth birthday in August 1999 provided a terrific chance to prepare a convention at ETH Zurich with the target of featuring the cutting-edge in quantity concept and geometry. some of the leaders within the topic have been introduced jointly to offer an account of analysis within the final century in addition to speculations for attainable extra learn. The papers during this quantity hide a huge spectrum of quantity concept together with geometric, algebrao-geometric and analytic elements. This quantity will entice quantity theorists, algebraic geometers, and geometers with a bunch theoretic heritage. notwithstanding, it's going to even be precious for mathematicians (in specific examine scholars) who're drawn to being proficient within the country of quantity idea at first of the twenty first century and in attainable advancements for the long run.
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Over three hundred sequences and plenty of unsolved difficulties and conjectures concerning them are awarded herein. The publication includes definitions, unsolved difficulties, questions, theorems corollaries, formulae, conjectures, examples, mathematical standards, and so forth. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, virtually primes, cellular periodicals, services, tables, prime/square/factorial bases, generalized factorials, generalized palindromes, and so on.
Extra resources for A Panorama of Number Theory or The View from Baker's Garden
Using his fundamental inequalities concerning linear forms in logarithms, Baker derived in the 1960s explicit upper bounds for the solutions of all these equations. These provided the ﬁrst general algorithms for the solutions of such equations and, in case of these equations, furnished an afﬁrmative answer to Hilbert’s famous 10th problem. Baker’s quantitative results were later improved and generalized by himself and others. g. the books Baker (1975) , Baker & Masser (1977), Baker (1988), Gy˝ory (1980b), Shorey & Tijdeman (1986), Smart (1998), Fel’dman & Nesterenko (1998) and the references given there.
53, 107– 186. Yu, Kunrui (1990), Linear forms in p-adic logarithms II, Compositio Math. 74, 15–113. Yu, Kunrui (1994), Linear forms in p-adic logarithms III, Compositio Math. 91, 241–276. Yu, Kunrui (1998), P-adic logarithmic forms and group varieties I, J. Reine Angew. Math. 502, 29–92. Yu, Kunrui (1999), p-adic logarithmic forms and group varieties II, Acta Arith. 89, 337–378. 3 Recent Progress on Linear Forms in Elliptic Logarithms Sinnou David and Noriko Hirata-Kohno 1 Introduction In this article, we describe recent progress on the theory of linear forms in logarithms associated with elliptic curves deﬁned over a number ﬁeld.
1965), On the units of an algebraic number ﬁeld, Illinois J. Math. 9, 584–589. Baker, A. (1966), Linear forms in the logarithms of algebraic numbers I, Mathematika 13, 204–216. Baker, A. (1967a), Linear forms in the logarithms of algebraic numbers II, Mathematika 14, 102–107. Baker, A. (1967b), Linear forms in the logarithms of algebraic numbers III, Mathematika 14, 220–228. Baker, A. (1968), Linear forms in the logarithms of algebraic numbers IV, Mathematika 15, 204–216. Baker, A. (1973), A sharpening of the bounds for linear forms in logarithms II, Acta Arith.