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71.
Given a polynomial with integer coefficients, we calculate the density of the set of primes modulo which the polynomial has a root. We also give a simple criterion to decide whether or not the polynomial has a root modulo every non-zero integer.
72.
Some congruence properties of the partition function are proved. 相似文献
73.
74.
75.
S. Raghavan 《Proceedings Mathematical Sciences》1987,97(1-3):263-276
For Ramanujan’s modular identities connected with his well-known partition congruences for the moduli 5 or 7, we had given,
in an earlier paper, natural and uniform proofs through the medium of modular forms. Analogous (modular) identities corresponding
to the (more difficult) case of the modulus 11 are provided here, with the consequent partition congruences; the relationship
with relevant results of N J Fine is also sketched. 相似文献
76.
Michael Reid 《Compositio Mathematica》2003,137(1):75-90
A refinement of the rank 1 Abelian Stark conjecture has been formulated by B.Gross. This conjecture predicts some
-adic analytic nature of a modification of the Stark unit. The conjecture makes perfect sense even when
is an Archimedean place. Here we consider the conjecture when
is a real place, and interpret it in terms of 2-adic properties of special values of L-functions. We prove the conjecture for CM extensions; here the original Stark conjecture is uninteresting, but the refined conjecture is nontrivial. In more generality, we show that, under mild hypotheses, if the subgroup of the Galois group generated by complex conjugations has less than full rank, then the refined conjecture implies that the Stark unit should be a square. This phenomenon has been discovered by Dummit and Hayes in a particular type of situation. We show that it should hold in much greater generality. 相似文献
77.
A special subclass of shear-free null congruences (SFC) is studied, with tangent vector field being a repeated principal null direction of the Weyl tensor. We demonstrate that this field is parallel with respect to an effective affine connection which contains the Weyl nonmetricity and the skew symmetric torsion. On the other hand, a Maxwell-like field can be directly associated with any special SFC, and the electric charge for bounded singularities of this field turns to be self-quantized. Two invariant differential operators are introduced which can be thought of as spinor analogues of the Beltrami operators and both nullify the principal spinor of any special SFC. 相似文献
78.
In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string
are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a
finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work. 相似文献
79.
We derive the generalized Raychauduri equation concepts of expansion, shear and vorticity. We give the Ricci tensor of a constant-curvature Randers–Finsler space metric whose first term is the Robertson–Walker metric.Dedicated to the memory of Professor Nikolaos Danikas. 相似文献
80.
《Discrete Mathematics》2022,345(1):112672
Recently, Andrews proved two conjectures of Beck related to ranks of partitions. Very recently, Chern established some results on weighted rank and crank moments and proved many Andrews-Beck type congruences. Motivated by Andrews and Chern's work, Lin, Peng and Toh proved a number of Andrews-Beck type congruences for k-colored partitions. At the end of their paper, Lin, Peng and Toh posed several conjectures on Andrews-Beck type congruences. In this paper, we confirm one of those conjectures based on some q-series identities. 相似文献