Seminar
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| Location: | SLMath: Baker Board Room |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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4:00pm: Vinay Kumaraswamy
Title: On correlations between class numbers of imaginary quadratic fields
Abstract: Let h(-d) denote the class number of the imaginary quadratic field Q(\sqrt{-d}). Moments of class numbers have been studied in the past, and are well understood. In this talk, I will speak about obtaining an asymptotic formula for the shifted sum \sum_{d \leq X} h(-d)h(-d-l), where l is a positive integer; the proof makes use of the smooth delta-symbol.
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4:30pm: Corina Panda
Title:
A generalization of a theorem of Hecke for SL_2(F_p) to fundamental discriminants
A generalization of a theorem of Hecke for SL_2(F_p) to fundamental discriminants
Abstract:
Let p > 3 be an odd prime, p ≡ 3 mod 4 and let π+, π− be the pair of cuspidal representations of SL2(Fp). It is well known by Hecke that the difference mπ+ − mπ− in the multiplicities of these two irreducible representations occurring in the space of weight 2 cusps forms with respect to the principal congruence subgroup Γ(p), equals the class number h(−p) of the imaginary quadratic field Q(\sqrt(−p)). We extend this result to all fundamental discriminants −D of imaginary quadratic fields Q( \sqrt(−D)). The proof uses the holomorphic Lefschetz number.