1,428 research outputs found
On the special values of certain L-series related to half-integral weight modular forms
Let h be a cuspidal Hecke eigenform of half-integral weight, and En/2+1/2 be Cohen’s Eisenstein series of weight n/2+1/2. For a Dirichlet character χ we define a certain linear combination R(χ)(s, h,En/+1/2) of the Rankin-Selberg convolution products of h and En/2+1/2 twisted by Dirichlet characters related with χ. We then prove a certain algebraicity result for R(χ)(l, h,En/2+1/2) with l integers
Non-vanishing of -functions associated to cusp forms of half-integral weight
In this article, we prove non-vanishing results for -functions associated
to holomorphic cusp forms of half-integral weight on average (over an
orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to
forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings
(Springer
On certain finiteness questions in the arithmetic of modular forms
We investigate certain finiteness questions that arise naturally when
studying approximations modulo prime powers of p-adic Galois representations
coming from modular forms. We link these finiteness statements with a question
by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms.
Specifically, we conjecture that for fixed N, m, and prime p with p not
dividing N, there is only a finite number of reductions modulo p^m of
normalized eigenforms on \Gamma_1(N). We consider various variants of our basic
finiteness conjecture, prove a weak version of it, and give some numerical
evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3:
restructered parts of the article; v4: minor corrections and change
Performance Criteria for Relational Database Normalization
The fourth normal form where data redundancy is eliminated is a more efficient construct for storage and user access
Virtually abelian K\"ahler and projective groups
We characterise the virtually abelian groups which are fundamental groups of
compact K\"ahler manifolds and of smooth projective varieties. We show that a
virtually abelian group is K\"ahler if and only if it is projective. In
particular, this allows to describe the K\"ahler condition for such groups in
terms of integral symplectic representations
Moduli interpretation of Eisenstein series
Let L >= 3. Using the moduli interpretation, we define certain elliptic
modular forms of level Gamma(L) over any field k where 6L is invertible and k
contains the Lth roots of unity. These forms generate a graded algebra R_L,
which, over C, is generated by the Eisenstein series of weight 1 on Gamma(L).
The main result of this article is that, when k=C, the ring R_L contains all
modular forms on Gamma(L) in weights >= 2. The proof combines algebraic and
analytic techniques, including the action of Hecke operators and nonvanishing
of L-functions. Our results give a systematic method to produce models for the
modular curve X(L) defined over the Lth cyclotomic field, using only exact
arithmetic in the L-torsion field of a single Q-rational elliptic curve E^0.Comment: 29 pages, amslatex. Version 6: corrected a sign misprint in equation
(4.6) (thanks to N. Mascot for pointing it out). Final accepted versio
Endomorphisms of superelliptic jacobians
Let K be a field of characteristic zero, n>4 an integer, f(x) an irreducible
polynomial over K of degree n, whose Galois group is doubly transitive simple
non-abelian group. Let p be an odd prime, Z[\zeta_p] the ring of integers in
the p-th cyclotomic field,
C_{f,p}:y^p=f(x) the corresponding superelliptic curve and J(C_{f,p}) its
jacobian. Assuming that either n=p+1 or p does not divide n(n-1), we prove that
the ring of all endomorphisms of J(C_{f,p}) coincides with Z[\zeta_p].Comment: Several typos have been correcte
Interpolated sequences and critical -values of modular forms
Recently, Zagier expressed an interpolated version of the Ap\'ery numbers for
in terms of a critical -value of a modular form of weight 4. We
extend this evaluation in two directions. We first prove that interpolations of
Zagier's six sporadic sequences are essentially critical -values of modular
forms of weight 3. We then establish an infinite family of evaluations between
interpolations of leading coefficients of Brown's cellular integrals and
critical -values of modular forms of odd weight.Comment: 23 pages, to appear in Proceedings for the KMPB conference: Elliptic
Integrals, Elliptic Functions and Modular Forms in Quantum Field Theor
- …