On a diophantine equation involving quadratic characters

Karl Dilcher

Compositio Mathematica (1986)

  • Volume: 57, Issue: 3, page 383-403
  • ISSN: 0010-437X

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Dilcher, Karl. "On a diophantine equation involving quadratic characters." Compositio Mathematica 57.3 (1986): 383-403. <http://eudml.org/doc/89760>.

@article{Dilcher1986,
author = {Dilcher, Karl},
journal = {Compositio Mathematica},
keywords = {finite number of solutions; primitive quadratic residue class character; generalized Bernoulli polynomials},
language = {eng},
number = {3},
pages = {383-403},
publisher = {Martinus Nijhoff Publishers},
title = {On a diophantine equation involving quadratic characters},
url = {http://eudml.org/doc/89760},
volume = {57},
year = {1986},
}

TY - JOUR
AU - Dilcher, Karl
TI - On a diophantine equation involving quadratic characters
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 57
IS - 3
SP - 383
EP - 403
LA - eng
KW - finite number of solutions; primitive quadratic residue class character; generalized Bernoulli polynomials
UR - http://eudml.org/doc/89760
ER -

References

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  1. [1] B.C. Berndt: Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications, J. Number Theory7 (1975) 413-445. Zbl0316.10023MR382187
  2. [2] J. Brillhart: On the Euler and Bernoulli polynomials, J. Reine Angew. Math.234 (1969) 45-64. Zbl0167.35401MR242790
  3. [3] B. Brindza: On S-integral solutions of the equation ym = f(x), Acta Math. Hung.44 (1984) 133-139. Zbl0552.10009MR759041
  4. [4] L. Carlitz: A conjecture concerning the Euler numbers, Amer. Math. Monthly69 (1962) 538-540. Zbl0105.26403MR1531734
  5. [5] K. Dilcher: Irreducibilty of generalized Bernoulli polynomials, preprint. Zbl0558.10012
  6. [6] K. Dilcher: Asymptotic behaviour of Bernoulli, Euler, and generalzed Bernoulli polynomials, to appear in J. Approx. Theory. Zbl0609.10008MR881502
  7. [7] R.J. Duffin: Algorithms for localizing roots of a polynomial and the Pisot Vijayaraghavan numbers, Pacific J. Math.74 (1978) 47-56. Zbl0381.12001MR480414
  8. [8] R. Ernvall: Generalized Bernoulli numbers, generalized irregular primes, and class numbers, Ann. Univ. Turku, Ser. AI, 178 (1979) 72 p. Zbl0403.12010MR533377
  9. [9] K. Györy, R. Tijdeman and M. Voorhoeve: On the equation 1k + 2k + ··· + xk = yz, Acta Arith.37 (1980), 233-240. Zbl0365.10014MR598878
  10. [10] K. Iwasawa: Lectures on p-acid L-functions, Princeton University Press (1972). Zbl0236.12001MR360526
  11. [11] D.E. Knuth and T.J. Buckholtz: Computation of tangent. Euler, and Bernoulli numbers. Math. Comp.21 (1967) 663-688. Zbl0178.04401MR221735
  12. [12] L.J. Mordell: Diophantine equations, Academic Press, London (1969). Zbl0188.34503MR249355
  13. [13] N. Nörlund: Vorlesungen über Differenzenrechung, Springer Verlag, Berlin (1924). 
  14. [14] G. Polya and G. Szegö: Aufgaben und Lehrsätze aus der Analysis, Springer Verlag, Berlin (1925). Zbl51.0173.01JFM51.0173.01
  15. [15] J.J. Schäffer: The equation 1p + 2p + 3p + ··· + np = mq, Acta Math.95 (1956) 155-189. Zbl0071.03702
  16. [16] M. Voorhoeve, K. Györy and R. Tijdeman: On the diophantine equation 1k + 2k + ··· + xk + R(x) = yz, Acta Math.143 (1979) 1-8. Zbl0426.10019MR523394

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