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# Search results

11,186 records were found.

## On the zeros of certain Poincar\'e series for $\Gamma_0^*(2)$ and $\Gamma_0^*(3)$

Comment: 12 pages. http://www2.math.kyushu-u.ac.jp/~j.shigezumi/

## Average equidistribution of Heegner points associated to the 3-part of the class group of imaginary quadratic fields

Comment: Updated references

## On Galois cohomology of unipotent algebraic groups over local fields

Comment: 11 pages, some typos are corrected; Introduction and Section 3 are revised; some remarks are added; main results are unchanged

## Sur les formules asymptotiques le long des Zl-extensions

In this paper we clarify some asymptotic formulas given by Jaulent-Maire, which relate orders of finite quotients of S-infinitesimal T-classes l-groups $Cl^S_T(K_n)$ associated to finite layers $K_n$ of a Zl-extension $K_\infty/K$ over a number field to the structural invariants of the Iwasawa module $X^S_T:=\varprojlim \Cl^S_T(K_n)$. We especially show that the lambda invariant $\tilde\lambda^S_T$ of those quotients sensibly differs from the structural invariant $\lambda^S_T$, and we illustrate this fact with explicit examples, where it can be made as large as desired, positive or negative.

## Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes

Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen Bracket, we extend this result to modular forms of half integral weight for primes $p \geq 5$. As applications of our main theorem we derive distribution properties, for modulo primes $p\geq5$, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newman's conjecture for overpartitions.

## $p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight

Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on $\Gamma_{0}(4N)$ for $N=1,2,4$. A proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications we obtain congruences of Borcherds exponents, congruences of quotient of Eisentein series and congruences of values of $L$-functions at a certain point are also studied. Furthermore, the congruences of the Fourier coefficients of Siegel modular forms on Maass Space are obtained using Ikeda lifting.

## On Some Subgroup Chains Related to Kneser's Theorem

A recent result of Balandraud shows that for every subset S of an abelian group G, there exists a non trivial subgroup H such that |TS| <= |T|+|S|-2 holds only if the stabilizer of TS contains H. Notice that Kneser's Theorem says only that the stabilizer of TS must be a non-zero subgroup. This strong form of Kneser's theorem follows from some nice properties of a certain poset investigated by Balandraud. We consider an analogous poset for nonabelian groups and, by using classical tools from Additive Number Theory, extend some of the above results. In particular we obtain short proofs of Balandraud's results in the abelian case.

Comment: 3 pages

## Test vectors for trilinear forms, when two representations are unramified and one is special

Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the space of G-invariant linear forms has dimension at most one. When a non zero linear form exists, one wants to find an element of V which is not in its kernel: this is a test vector. Gross and Prasad found explicit test vectors for some triple of representations. In this paper, others are found, and they almost complete the case when the conductor of each representation is at most 1.

## On the weight structure of cyclic codes over $GF(q)$, $q>2$

Comment: 11 pages, no figures