A class number congruence for cyclotomic fields and their subfields
Tauno Metsänkylä (1973)
Acta Arithmetica
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Tauno Metsänkylä (1973)
Acta Arithmetica
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Štefan Porubský (1984)
Czechoslovak Mathematical Journal
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Gong, Sherry, Kominers, Scott Duke (2010)
Integers
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William Y. C. Chen, Ernest X. W. Xia (2014)
Acta Arithmetica
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Let p̅(n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that p̅(40n+35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for p̅(40n+35) modulo 5. Using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we prove the congruence p̅(40n+35) ≡ 0 (mod 5) for n ≥ 0. Combining this congruence and the congruence p̅(4n+3)...
A. Schinzel (2015)
Acta Arithmetica
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Assertions on the congruence f(x) + g(y) + c ≡ 0 (mod xy) made without proof by Mordell in his paper in Acta Math. 88 (1952) are either proved or disproved.
Andrzej Schinzel (1982)
Acta Arithmetica
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Ilya Sh. Slavutskii (2000)
Revista Matemática Iberoamericana
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The study of class number invariants of absolute abelian fields, the investigation of congruences for special values of L-functions, Fourier coefficients of half-integral weight modular forms, Rubin's congruences involving the special values of L-functions of elliptic curves with complex multiplication, and many other problems require congruence properties of the generalized Bernoulli numbers (see [16]-[18], [12], [29], [3], etc.). The first steps in this direction can be found in the...
Andrzej Schinzel (1977)
Acta Arithmetica
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F. Beukers (1986-1987)
Groupe de travail d'analyse ultramétrique
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