Traces of Hecke operators in level 1 and Gaussian hypergeometric functions
نویسندگان
چکیده
منابع مشابه
Gaussian Hypergeometric Functions and Traces of Hecke Operators
We establish a simple inductive formula for the trace Tr k (Γ0(8), p) of the p-th Hecke operator on the space S k (Γ0(8)) of newforms of level 8 and weight k in terms of the values of 3F2-hypergeometric functions over the finite field Fp. Using this formula when k = 6, we prove a conjecture of Koike relating Tr 6 (Γ0(8), p) to the values 6F5(1)p and 4F3(1)p. Furthermore, we find new congruences...
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We study the action of the Hecke operators Un on the set of hypergeometric functions, as well as on formal power series. We show that the spectrum of these operators on the set of hypergeometric functions is the set {na : n ∈ N and a ∈ Z}, and that the polylogarithms play a dominant role in the study of the eigenfunctions of the Hecke operators Un on the set of hypergeometric functions. As a co...
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We investigate the combinatorial properties of the traces of the nth Hecke operators on the spaces of weight 2k cusp forms of level N. We establish examples in which these traces are expressed in terms of classical objects in enumerative combinatorics (e.g., tilings and Motzkin paths). We establish in general that Hecke traces are explicit rational linear combinations of values of Gegenbauer (a...
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Abstract. We investigate the combinatorial properties of the traces of the n-th Hecke operators on the spaces of weight 2k cusp forms of level N . We establish examples in which these traces are expressed in terms of classical objects in enumerative combinatorics (e.g. tilings and Motzkin paths). We establish in general that Hecke traces are explicit rational linear combinations of values of Ge...
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Using a reformulation of the Eichler-Selberg trace formula, due to Frechette, Ono and Papanikolas, we consider the problem of the vanishing (resp. non-vanishing) of traces of Hecke operators on spaces of even weight cusp forms with trivial Nebentypus character. For example, we show that for a fixed operator and weight, the set of levels for which the trace vanishes is effectively computable. Al...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11540-0