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971.
We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for some combinatorial functions which may be expressed in terms of the second moments. Finally, we establish a congruence modulo 3 involving one such combinatorial function and the Hurwitz class number H(n). 相似文献
972.
Nigel P. Byott 《Journal of Number Theory》2009,129(1):84-101
Ramification invariants are necessary, but not in general sufficient, to determine the Galois module structure of ideals in local number field extensions. This insufficiency is associated with elementary abelian extensions, where one can define a refined ramification filtration—one with more ramification breaks [Nigel P. Byott, G. Griffith Elder, New ramification breaks and additive Galois structure, J. Théor. Nombres Bordeaux 17 (1) (2005) 87-107]. The first refined break number comes from the usual ramification filtration and is therefore necessary. Here we study the second refined break number. 相似文献
973.
Veronika Trnková 《Journal of Number Theory》2009,129(1):28-35
We compute the index of a certain extension of Sinnott's group of circular units in the group of all units of a bicyclic field. From this index we obtain some divisibility properties for class numbers of bicyclic fields. 相似文献
974.
Let L be a totally real field of strict class number one and let OL be its ring of integers. Let p be a rational prime which is unramified in L. We consider the distance between two superspecial abelian varieties with real multiplication in characteristic p, where by “distance” we mean the minimal degree of an OL-isogeny. We give upper and lower bounds on the distance between superspecial abelian varieties with real multiplication by L in characteristic p in terms of p and the degree and discriminant of L. 相似文献
975.
Guangshi Lü 《Journal of Number Theory》2009,129(2):488-494
Recently Blomer showed that if α(n) denote the normalized Fourier coefficients of any holomorphic cusp form f with integral weight, then
976.
Amitabha Tripathi 《Journal of Number Theory》2009,129(7):1805-1811
Text
Let s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane and Sze regarding the largest size of a partition that is simultaneously s-core and t-core by solving an equivalent problem concerning sets S of positive integers with the property that for n∈S, n−s∈S whenever n?s and n−t∈S whenever n?t.Video
For a video summary of this paper, please visit http://www.youtube.com/watch?v=o1OEug8LryU. 相似文献977.
Chieh-Yu Chang 《Journal of Number Theory》2009,129(3):729-1154
We give a refinement of the linear independence criterion over function fields developed by Anderson, Brownawell and Papanikolas [Greg W. Anderson, W. Dale Brownawell, Matthew A. Papanikolas, Determination of the algebraic relations among special Γ-values in positive characteristic, Ann. of Math. 160 (2004) 237-313]. As a consequence, a function field analogue of the Siegel-Shidlovskii theorem is derived. 相似文献
978.
Let φ be a Drinfeld A-module of arbitrary rank and arbitrary characteristic over a finitely generated field K, and set GK=Gal(Ksep/K). Let E=EndK(φ). We show that for almost all primes p of A the image of the group ring A[GK] in EndA(Tp(φ)) is the commutant of E. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p](Ksep) of φ is absolutely irreducible for almost all p. 相似文献
979.
Let ψ(x) denote the digamma function. We study the linear independence of ψ(x) at rational arguments over algebraic number fields. We also formulate a variant of a conjecture of Rohrlich concerning linear independence of the log gamma function at rational arguments and report on some progress. We relate these conjectures to non-vanishing of certain L-series. 相似文献
980.
Nikita Sidorov 《Journal of Number Theory》2009,129(4):741-754
Let q∈(1,2); it is known that each x∈[0,1/(q−1)] has an expansion of the form with an∈{0,1}. It was shown in [P. Erd?s, I. Joó, V. Komornik, Characterization of the unique expansions and related problems, Bull. Soc. Math. France 118 (1990) 377-390] that if , then each x∈(0,1/(q−1)) has a continuum of such expansions; however, if , then there exist infinitely many x having a unique expansion [P. Glendinning, N. Sidorov, Unique representations of real numbers in non-integer bases, Math. Res. Lett. 8 (2001) 535-543]. In the present paper we begin the study of parameters q for which there exists x having a fixed finite number m>1 of expansions in base q. In particular, we show that if q<q2=1.71…, then each x has either 1 or infinitely many expansions, i.e., there are no such q in . On the other hand, for each m>1 there exists γm>0 such that for any q∈(2−γm,2), there exists x which has exactly m expansions in base q. 相似文献