On a diophantine equation involving quadratic characters
Compositio Mathematica, Volume 57 (1986) no. 3, p. 383-403
@article{CM_1986__57_3_383_0,
     author = {Dilcher, Karl},
     title = {On a diophantine equation involving quadratic characters},
     journal = {Compositio Mathematica},
     publisher = {Martinus Nijhoff Publishers},
     volume = {57},
     number = {3},
     year = {1986},
     pages = {383-403},
     zbl = {0584.10008},
     mrnumber = {829328},
     language = {en},
     url = {http://www.numdam.org/item/CM_1986__57_3_383_0}
}
Dilcher, Karl. On a diophantine equation involving quadratic characters. Compositio Mathematica, Volume 57 (1986) no. 3, pp. 383-403. http://www.numdam.org/item/CM_1986__57_3_383_0/

[1] B.C. Berndt: Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications, J. Number Theory 7 (1975) 413-445. | MR 382187 | Zbl 0316.10023

[2] J. Brillhart: On the Euler and Bernoulli polynomials, J. Reine Angew. Math. 234 (1969) 45-64. | MR 242790 | Zbl 0167.35401

[3] B. Brindza: On S-integral solutions of the equation ym = f(x), Acta Math. Hung. 44 (1984) 133-139. | MR 759041 | Zbl 0552.10009

[4] L. Carlitz: A conjecture concerning the Euler numbers, Amer. Math. Monthly 69 (1962) 538-540. | MR 1531734 | Zbl 0105.26403

[5] K. Dilcher: Irreducibilty of generalized Bernoulli polynomials, preprint. | Zbl 0558.10012

[6] K. Dilcher: Asymptotic behaviour of Bernoulli, Euler, and generalzed Bernoulli polynomials, to appear in J. Approx. Theory. | MR 881502 | Zbl 0609.10008

[7] R.J. Duffin: Algorithms for localizing roots of a polynomial and the Pisot Vijayaraghavan numbers, Pacific J. Math. 74 (1978) 47-56. | MR 480414 | Zbl 0381.12001

[8] R. Ernvall: Generalized Bernoulli numbers, generalized irregular primes, and class numbers, Ann. Univ. Turku, Ser. AI, 178 (1979) 72 p. | MR 533377 | Zbl 0403.12010

[9] K. Györy, R. Tijdeman and M. Voorhoeve: On the equation 1k + 2k + ··· + xk = yz, Acta Arith. 37 (1980), 233-240. | MR 598878 | Zbl 0365.10014

[10] K. Iwasawa: Lectures on p-acid L-functions, Princeton University Press (1972). | MR 360526 | Zbl 0236.12001

[11] D.E. Knuth And T.J. Buckholtz: Computation of tangent. Euler, and Bernoulli numbers. Math. Comp. 21 (1967) 663-688. | MR 221735 | Zbl 0178.04401

[12] L.J. Mordell: Diophantine equations, Academic Press, London (1969). | MR 249355 | Zbl 0188.34503

[13] N. Nörlund: Vorlesungen über Differenzenrechung, Springer Verlag, Berlin (1924).

[14] G. Polya and G. Szegö: Aufgaben und Lehrsätze aus der Analysis, Springer Verlag, Berlin (1925). | JFM 51.0173.01

[15] J.J. Schäffer: The equation 1p + 2p + 3p + ··· + np = mq, Acta Math. 95 (1956) 155-189. | Zbl 0071.03702

[16] M. Voorhoeve, K. Györy and R. Tijdeman: On the diophantine equation 1k + 2k + ··· + xk + R(x) = yz, Acta Math. 143 (1979) 1-8. | MR 523394 | Zbl 0426.10019