共查询到20条相似文献,搜索用时 31 毫秒
1.
Matthew Boylan 《Journal of Number Theory》2003,98(2):377-389
Let F(z)=∑n=1∞a(n)qn denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that
2.
Guangshi Lü 《Journal of Number Theory》2009,129(11):2790-2800
Let λ(n) be the nth normalized Fourier coefficient of a holomorphic Hecke eigencuspform f(z) of even integral weight k for the full modular group. In this paper we are able to prove the following results.
- (i)
- For any ε>0, we have
3.
Matija Kazalicki 《Journal of Number Theory》2008,128(6):1662-1669
For every positive integer m, there is a unique Drinfeld modular function, holomorphic on the Drinfeld upper-half plane, jm(z) with the following t-expansion
4.
Let (|q|<1). For k∈N it is shown that there exist k rational numbers A(k,0),…,A(k,k−1) such that
5.
6.
Eric Mortenson 《Journal of Number Theory》2003,99(1):139-147
Fernando Rodriguez-Villegas has been studying hypergeometric families of Calabi-Yau manifolds, and from his investigations he has found (numerically) many possible supercongruences. For example, he conjectures for every odd prime p that
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8.
In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
9.
Thomas Stoll 《Journal of Number Theory》2008,128(5):1157-1181
We characterize decomposition over C of polynomials defined by the generalized Dickson-type recursive relation (n?1)
10.
Hao Pan 《Journal of Number Theory》2008,128(6):1646-1654
Let e?1 and b?2 be integers. For a positive integer with 0?aj<b, define
11.
Tapani Matala-aho 《Journal of Number Theory》2009,129(5):1044-1055
We shall consider arithmetical properties of the q-continued fractions
12.
Yong-Gao Chen 《Journal of Number Theory》2003,100(2):326-331
Let p1,p2,… be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given , there exist infinitely many positive integers n with
13.
Zhi-Wei Sun 《Discrete Mathematics》2008,308(18):4231-4245
In this paper we study recurrences concerning the combinatorial sum and the alternate sum , where m>0, n?0 and r are integers. For example, we show that if n?m-1 then
14.
B.V. Petrenko 《Journal of Pure and Applied Algebra》2003,178(3):297-306
Let denote a finite field with r elements. Let q be a power of a prime, and p1,p2, p3 be distinct primes. Put
15.
Yan Qu 《Journal of Number Theory》2010,130(3):786-802
Let m?2 be an integer, and π an irreducible unitary cuspidal representation for GLm(AQ), whose attached automorphic L-function is denoted by L(s,π). Let be the sequence of coefficients in the Dirichlet series expression of L(s,π) in the half-plane Rs>1. It is proved in this paper that, if π is such that the sequence is real, then there are infinitely many sign changes in the sequence , and the first sign change occurs at some , where Qπ is the conductor of π, and the implied constant depends only on m and ε. This generalizes the previous results for GL2. A result of the same quality is also established for , the sequence of coefficients in the Dirichlet series expression of in the half-plane Rs>1. 相似文献
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17.
M.Z. Garaev 《Journal of Number Theory》2007,125(1):201-209
For a class of strictly increasing real valued functions f(n) we obtain an upper bound for the number of solutions of the equation
18.
Zhi-Wei Sun 《Journal of Number Theory》2011,131(12):2387-2397
The nth Delannoy number and the nth Schröder number given by
19.
Zhi-Hong Sun 《Journal of Number Theory》2008,128(2):280-312
Let [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine , , and in terms of Euler and Bernoulli numbers. For example, we have
20.
In 1964, S. Chowla asked if there is a non-zero integer-valued function f with prime period p such that f(p)=0 and