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1.
Goran Mui? 《Journal of Number Theory》2010,130(7):1488-1511
In this paper we study the construction and non-vanishing of cuspidal modular forms of weight m?3 for arbitrary Fuchsian groups of the first kind. We give a spanning set for the space of cuspidal modular forms Sm(Γ) of weight m?3 in a uniform way which does not depend on the fact that Γ has cusps or not. 相似文献
2.
The principal thrust of this investigation is to provide families of quadratic polynomials , where ek2−fk2C=n (for any given nonzero integer n) satisfying the property that for any , the period length of the simple continued fraction expansion of is constant for fixed k and limk→∞?k=∞. This generalizes, and completes, numerous results in the literature, where the primary focus was upon |n|=1, including the work of this author, and coauthors, in Mollin (Far East J. Math. Sci. Special Vol. 1998, Part III, 257-293; Serdica Math. J. 27 (2001) 317) Mollin and Cheng (Math. Rep. Acad. Sci. Canada 24 (2002) 102; Internat Math J 2 (2002) 951) and Mollin et al. (JP J. Algebra Number Theory Appl. 2 (2002) 47). 相似文献
3.
In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the
following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients
at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the p-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigenforms. We also show that
there is an automorphic L-function over whose local factors agree with those of the l-adic Scholl representations attached to the space of noncongruence cusp forms.
The research of the second author was supported in part by an NSA grant #MDA904-03-1-0069 and an NSF grant #DMS-0457574. Part
of the research was done when she was visiting the National Center for Theoretical Sciences in Hsinchu, Taiwan. She would
like to thank the Center for its support and hospitality. The third author was supported in part by an NSF-AWM mentoring travel
grant for women. She would further thank the Pennsylvania State University and the Institut des Hautes études Scientifiques
for their hospitality. 相似文献
4.
G. Lomadze 《Georgian Mathematical Journal》1995,2(2):189-199
Two classes of entire modular forms of weight 5 and two of weight 6 are constructed for the congruence subgroup 0(4N). The constructed modular forms as well as the modular forms from [1] will be helpful in the theory of representation of numbers by the quadratic forms in 10 and 12 variables. 相似文献
5.
In recent work, Hickerson and the author demonstrated that it is useful to think of Appell–Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell–Lerch sums. In this sense, Appell–Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers–Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral q-series with mixed mock modular behaviour. In subsequent work we see that our bilateral series are well-suited for computing radial limits of Ramanujan's mock theta functions. 相似文献
6.
Yen-Mei J. Chen 《Journal of Number Theory》2008,128(7):2138-2158
Gauss made two conjectures about average values of class numbers of orders in quadratic number fields, later on proven by Lipschitz and Siegel. A version for function fields of odd characteristic was established by Hoffstein and Rosen. In this paper, we extend their results to the case of even characteristic. More precisely, we obtain formulas of average values of L-functions associated to orders in quadratic function fields over a constant field of characteristic two, and then derive formulas of average class numbers of these orders. 相似文献
7.
Ö. J. Rödseth 《BIT Numerical Mathematics》1994,34(3):451-454
Using only the most simple properties of the finite field
, we give a short proof of Riesel's primality test for integers of the formN=h·2
n
–1. 相似文献
8.
In this paper, we study congruence properties of modular forms in various ways. By proving a weight-dependent congruence property of modular forms, we give some sufficient conditions, in terms of the weights of modular forms, for a modular form to be non-p-ordinary. As applications of our main theorem we derive a linear relation among coefficients of new forms. Furthermore, congruence relations among special values of Dedekind zeta functions of real quadratic fields are derived. 相似文献
9.
Jürgen Elstrodt 《manuscripta mathematica》2006,121(4):457-459
We give a very simple proof of a classical transformation formula for the Dedekind eta function. This proof is a simplified version of an approach suggested by H. Petersson. 相似文献
10.
Let p>3 be a prime. We consider j-zeros of Eisenstein series Ek of weights k=p−1+Mpa(p2−1) with M,a?0 as elements of . If M=0, the j-zeros of Ep−1 belong to Qp(ζp2−1) by Hensel's lemma. Call these j-zeros p-adic liftings of supersingular j-invariants. We show that for every such lifting u there is a j-zero r of Ek such that ordp(r−u)>a. Applications of this result are considered. The proof is based on the techniques of formal groups. 相似文献
11.
Yuk-Kam Lau 《Archiv der Mathematik》2003,81(2):169-174
We establish a mean square estimate on the weight aspect for
symmetric square L-functions at every point
on the critical line.
Received: 15 February 2002 相似文献
12.
In this paper, we give parametric families of both real and complex quadratic number fields whose class group has 3-rank at least 2. As a consequence, we obtain that for all large positive real numbers x, the number of both real and complex quadratic fields whose class group has 3-rank at least 2 and absolute value of the discriminant ?x is >cx1/3, where c is some positive constant. 相似文献
13.
Stéfane Fermigier 《Mathematische Annalen》1996,306(1):247-256
Sans résumé
Je remercie Jean-François Mestre, mon directeur de thèse, dont les idées sont à l'origine de ce travail, ainsi que Laurent Clozel, Guy Henniart et Jean-Pierre Labesse qui ont contribué par leur aide précieuse à son bon déroulement 相似文献
14.
Dongho Byeon 《manuscripta mathematica》2006,120(2):211-215
We shall show that the number of real quadratic fields whose absolute discriminant is ≤ x and whose class number is divisible by 5 or 7 is
improving the existing best known bound for g = 5 and for g = 7 of Yu (J Number Theory 97:35–44, 2002).This work was supported by KRF-R08-2003-000-10243-0 and partially by KRF-2005-070-C00004. 相似文献
15.
Igor E. Shparlinski 《Archiv der Mathematik》2005,85(6):508-513
We give lower bounds on the number of distinct values of the Ramanujan function τ(n), n ≦ x, and on the number of distinct residues of τ(n), n ≦ x, modulo a prime ℓ. We also show that for any prime ℓ the values τ(n), n ≦ ℓ4, form a finite additive basis modulo ℓ.
Received: 6 October 2004 相似文献
16.
Dongho Byeon 《Journal of Number Theory》2011,131(8):1513-1529
Let m be a positive integer and fm(x) be a polynomial of the form fm(x)=x2+x−m. We call a polynomial fm(x) a Rabinowitsch polynomial if for and consecutive integers x=x0,x0+1,…,x0+s−1, |fm(x)| is either 1 or prime. In this paper, we show that there are exactly 14 Rabinowitsch polynomials fm(x). 相似文献
17.
In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by different methods, these coincide with the classical Shintani lifts when restricted to the space of cusp forms. As a side effect, this gives the coefficients of the classical Shintani lifts as new cycle integrals. This yields new formulas for the L-values of Hecke eigenforms. When restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms, the Shintani lifts introduce a definition of weakly holomorphic Hecke eigenforms. Along the way, auxiliary lifts are constructed from the space of harmonic weak Maass forms which yield a “fractional derivative” from the space of half-integral weight harmonic weak Maass forms to half-integral weight weakly holomorphic modular forms. This fractional derivative complements the usual ξ-operator introduced by Bruinier and Funke. 相似文献
18.
In this paper, we shall give a new relation between the arithmetic of quaternion algebras and modular forms; we shall express
the type numberT
q, N
of a split order of type (q, N) as the sums of dimensions of some subspaces of the space of cusp forms of weight 2 with respect to Γ0(qN) which are common eigenspaces of Atkin-Lehner's involutions. 相似文献
19.
Recently by using the theory of modular forms and the Riemann zeta-function, Lü improved the estimates for the error term in a divisor problem related to the Epstein zeta-function established by Sankaranarayanan. In this short note, we are able to further sharpen some results of Sankaranarayanan and of Lü, and to establish corresponding Ω-estimates. 相似文献
20.
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