Related papers: A note on the trace formula
We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of…
We give a short proof of the trace formula for Hecke operators on modular forms for the modular group, using the action of Hecke operators on the space of period polynomials.
In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Here we specialize it to the congruence subgroups $\Gamma_0(N)$…
We derive an explicit formula for the trace of an arbitrary Hecke operator on spaces of twist-minimal holomorphic cusp forms with arbitrary level and character, and weight at least 2. We show that this formula provides an efficient way of…
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions are in terms of hypergeometric character sums over finite…
We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applications to the analytic theory of elliptic curves over a finite…
We present here simple trace formulas for Hecke operators $T_k(p)$ for all $p>3$ on $S_k(\Gamma_0(3))$ and $S_k(\Gamma_0(9))$, the spaces of cusp forms of weight $k$ and levels 3 and 9. These formulas can be expressed in terms of special…
We prove multiplicity one for vector valued holomorphic Siegel modular forms of weights greater or equal to 3 and the full Siegel modular group and give a trace formula for the action of the Hecke operators T(p) in the regular cases.
In this paper we give a trace formula for Hecke operators acting on the cohomology of a Fuchsian group of finite covolume, with coefficients in a module $V$. The proof is based on constructing an operator whose trace on $V$ equals the…
We provide formulas for traces of p-th Hecke operators in level 1 in terms of values of finite field 2F1-hypergeometric functions, extending previous work of the author to all odd primes p, instead of only those p=1 (mod 12). We first give…
We study traces of Hecke operators on spaces of elliptic cusp forms and Drinfeld cusp forms and show that, modulo any prime power, these traces are periodic in the weight.
We specialize the Eichler-Selberg trace formula to obtain trace formulas for the prime-to-level Hecke action on cusp forms for certain congruence groups of arbitrary level. As a consequence, we determine the asymptotic in the prime p of the…
Let G be a reductive algebraic group over Q, and suppose that Gamma is an arithmetic subgroup of G(R) defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in…
In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case $A = \mathbb{F}_q[T]$. We deduce closed-form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and…
The present paper deals with Atkin-Lehner theory for Drinfeld modular forms. We provide an equivalent definition of $\mathfrak{p}$-newforms (which makes computations easier) and commutativity results between Hecke operators and Atkin-Lehner…
In this paper, for a square-free integer l>1, a even positive integer k and a positive integer N, we give a trace formula of the Hecke operator T(l) on the space S_k^0(N) of all newforms of weight k and level \Gamma_0(N). Moreover, we give…
In previous work, we gave a local formula for the index of Heisenberg elliptic operators on contact manifolds. We constructed a cocycle in periodic cyclic cohomology which, when paired with the Connes-Chern character of the principal…
We develop a method for describing the Galois action on the superspecial locus of the Siegel moduli space in characteristic $p$. Using this description, we give a modern treatment for the results of Ibukiyama and Katsura [Compos. Math.,…
Motivated by recent advances in Catalan combinatorics, we study special values of the standard trace on affine Hecke algebras. Starting from a generating function for this trace calculated by Opdam, we use the theory of Szenes and Vergne to…
For weighted Bergman spaces on the unit disk, we give trace formulas of semicommutators of Toeplitz operators with $\mathscr{C}^2(\overline{\mathbb{D}})$ symbols. We generalize this formula to weighted Bergman spaces on the unit ball in…