On diophantine equations involving sums of powers with quadratic characters as coefficients, II

Jerzy Urbanowicz

Compositio Mathematica (1996)

  • Volume: 102, Issue: 2, page 125-140
  • ISSN: 0010-437X

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Urbanowicz, Jerzy. "On diophantine equations involving sums of powers with quadratic characters as coefficients, II." Compositio Mathematica 102.2 (1996): 125-140. <http://eudml.org/doc/90449>.

@article{Urbanowicz1996,
author = {Urbanowicz, Jerzy},
journal = {Compositio Mathematica},
keywords = {sums of powers; generalized Bernoulli numbers; generalized Bernoulli polynomials; class number; exponential diophantine equations},
language = {eng},
number = {2},
pages = {125-140},
publisher = {Kluwer Academic Publishers},
title = {On diophantine equations involving sums of powers with quadratic characters as coefficients, II},
url = {http://eudml.org/doc/90449},
volume = {102},
year = {1996},
}

TY - JOUR
AU - Urbanowicz, Jerzy
TI - On diophantine equations involving sums of powers with quadratic characters as coefficients, II
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 102
IS - 2
SP - 125
EP - 140
LA - eng
KW - sums of powers; generalized Bernoulli numbers; generalized Bernoulli polynomials; class number; exponential diophantine equations
UR - http://eudml.org/doc/90449
ER -

References

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  1. 1 Brindza, B.: On S-integral solutions of the equation f(x) = y m, Acta Math. Acad. Sci. Hungar.44 (1984) 133-139. Zbl0552.10009MR759041
  2. 2 Dilcher, K.: On a diophantine equation involving quadratic characters, Compositio Math.57 (1986) 383-403. Zbl0584.10008MR829328
  3. 3 Leveque, W.J.: On the equation ym = f(x), Acta Arith.9 (1964) 209-219. Zbl0127.27201MR169813
  4. 4 Schinzel, A. and Tijdeman, R.: On the equation ym = f(x), Acta Arith.31 (1976) 199-204. Zbl0303.10016MR422150
  5. 5 Urbanowicz, J.: On the 2-primary part of a conjecture of Birch-Tate, Acta Arith.43 (1983) 69-81, and Corr. 64 (1993). Zbl0836.11037MR730849
  6. 6 Urbanowicz, J.: Connections between B2, χ for even quadratic characters χ and class numbers of appropriate imaginary quadratic fields, I, Compositio Math. 75 (1990) 247-270. Zbl0706.11058
  7. 7 Urbanowicz, J.: On some new congruences between generalized Bernoulli numbers, II, Publications Math. de la Fac. des Sci. de Besançon, Theorie des Nombres, Années 1990/91. Zbl0748.11018
  8. 8 Urbanowicz, J.: On diophantine equations involving sums of powers with quadratic characters as coefficients, I, Compositio Math.92 (1994) 249-271. Zbl0810.11017MR1286126
  9. 9 Voorhoeve, M., Györy, K. and Tijdeman, R.: On the diophantine equation 1k+2 k+...+xk+ R(x) = yz, Acta Math. 143 (1979) 1-8 and Corr. 159 (1987) 151-152. Zbl0632.10017MR523394

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