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

Compositio Mathematica (1994)

- Volume: 92, Issue: 3, page 249-271
- ISSN: 0010-437X

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topUrbanowicz, Jerzy. "On diophantine equations involving sums of powers with quadratic characters as coefficients, I." Compositio Mathematica 92.3 (1994): 249-271. <http://eudml.org/doc/90306>.

@article{Urbanowicz1994,

author = {Urbanowicz, Jerzy},

journal = {Compositio Mathematica},

keywords = {exponential diophantine equations; Bernoulli polynomials; superelliptic equations},

language = {eng},

number = {3},

pages = {249-271},

publisher = {Kluwer Academic Publishers},

title = {On diophantine equations involving sums of powers with quadratic characters as coefficients, I},

url = {http://eudml.org/doc/90306},

volume = {92},

year = {1994},

}

TY - JOUR

AU - Urbanowicz, Jerzy

TI - On diophantine equations involving sums of powers with quadratic characters as coefficients, I

JO - Compositio Mathematica

PY - 1994

PB - Kluwer Academic Publishers

VL - 92

IS - 3

SP - 249

EP - 271

LA - eng

KW - exponential diophantine equations; Bernoulli polynomials; superelliptic equations

UR - http://eudml.org/doc/90306

ER -

## References

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- [2] K. Dilcher: On a diophantine equation involving quadratic characters. Compositio Math.57 (1986) 383-403. Zbl0584.10008MR829328
- [3] W.J. Leveque: On the equation ym = f(x). Acta Arith.9 (1964) 209-219. Zbl0127.27201MR169813
- [4] A. Schinzel and R. Tijdeman: On the equation ym = f(x). Acta Arith.31 (1976) 199-204. Zbl0303.10016MR422150
- [5] J. Urbanowicz: On the 2-primary part of a conjecture of Birch-Tate. Acta Arith.43 (1983) 69-81 and Corr., to appear. Zbl0529.12008MR730849
- [6] J. Urbanowicz: 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] J. Urbanowicz: On some new congruences between generalized Bernoulli numbers. I. Publications Math. de la Fac. des Sci. de Besançon, Theorie des Nombres, Années 1990/ 1991. Zbl0748.11017
- [8] M. Voorhoeve, K. Györy and R. Tijdeman: On the diophantine equation 1k + 2k + ··· + xk + R(x) = y z. Acta Math. 143 (1979) 1-8 and Corr. 159 (1987) 151-152. Zbl0632.10017MR906528
- [9] L. Washington: Introduction to Cyclotomic Fields. Springer-Verlag, Berlin, Heidelberg, New York, 1982. Zbl0484.12001MR718674
- [10] A. Wiles: The Iwasawa conjecture for totally real fields. Ann. of Math.131 (1990) 493-540. Zbl0719.11071MR1053488

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