Beukers' integrals and Apéry's recurrences.
Beweis, dass jede Covariante und Invariante einer binären Form eine ganze Function mit numerischen Coefficienten einer endlichen Anzahl solcher Formen ist.
Beweis der Transcendenz der Zahl e.
Beweis der Transcendenz der Zahl e
Beweis des Reciprocitätengesetzes für die quadratischen Reste. (Aus eine Aufsatze in No. XXIII der Sitzungsberichte der Berliner Akademie 1884).
Beweis des Reziprozitatsgesetzes für quadratische Reste
Beweis des Satzes, dass jede eigentlich primitive quadratische Form unendlich viele Primzahlen darzustellen fähig ist
Beweis des Satzes, daß sich eine jede ganze Zahl als Summe von höchstens neun positiven Kuben darstellen läßt
Beweis einer Erweiterung des Satzes von Goldbach-Vinogradov.
Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem). Dem Andenken an Hermann Minkowski gewidmet.
Beyond two criteria for supersingularity: coefficients of division polynomials
Let be a cubic, monic and separable polynomial over a field of characteristic and let be the elliptic curve given by . In this paper we prove that the coefficient at in the –th division polynomial of equals the coefficient at in . For elliptic curves over a finite field of characteristic , the first coefficient is zero if and only if is supersingular, which by a classical criterion of Deuring (1941) is also equivalent to the vanishing of the second coefficient. So the zero loci...
BG-ranks and 2-cores.
Biases in the Shanks-Rényi prime number race.
Bicyclotomic polynomials and impossible intersections
In a recent paper we proved that there are at most finitely many complex numbers such that the points and are both torsion on the Legendre elliptic curve defined by . In a sequel we gave a generalization to any two points with coordinates algebraic over the field and even over . Here we reconsider the special case and with complex numbers and .
Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))
We determine all modular curves X(N) (with N ≥ 7) that are hyperelliptic or bielliptic. We also give a proof that the automorphism group of X(N) is PSL₂(ℤ/Nℤ), whence it coincides with the normalizer of Γ(N) in PSL₂(ℝ) modulo ±Γ(N).
Bielliptic modular curves X₁(N)
Bihomogeneous forms in many variables
We count integer points on varieties given by bihomogeneous equations using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in using the standard approach for homogeneous varieties. Also, we consider counting functions where not all the variables have to lie in intervals of the same size, which arises as a natural question in the setting of bihomogeneous varieties.
Bihyperbolic numbers of the Fibonacci type and their idempotent representation
In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.
Bijections and congruences for generalizations of partition identities of Euler and Guy.
Bijective proofs of parity theorems for partition statistics.