Rational values of Weierstrass zeta functions
| Autor: | Margaret E. M. Thomas, Gareth Jones |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Pure mathematics Weierstrass functions General Mathematics 010102 general mathematics Multiplicative function Algebraic number field 01 natural sciences Riemann zeta function Arithmetic zeta function symbols.namesake Weierstrass zeta functions counting irrationality Bounded function 0103 physical sciences Weierstrass factorization theorem symbols 010307 mathematical physics 0101 mathematics Algebraic number ddc:510 Mathematics |
| Popis: | We answer a question of Masser by showing that for the Weierstrass zeta function ζ corresponding to a given lattice Λ, the density of algebraic points of absolute multiplicative height bounded byTand degree bounded byklying on the graph of ζ, restricted to an appropriate domain, does not exceedc(logT)15for an effective constant c > 0 depending onkand on Λ. Using different methods, we also give two bounds of the same form for the density of algebraic points of bounded height in a fixed number field lying on the graph of ζ restricted to an appropriate subset of (0, 1). In one case the constant c can be shown not to depend on the choice of lattice; in the other, the exponent can be improved to 12. |
| Databáze: | OpenAIRE |
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