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• W2913571004 abstract "We formulate a thermodynamical approach to the study of distribution of modular symbols, motivated by the work of Baladi-Vall'ee. We introduce the modular partitions of continued fractions and observe that the statistics for modular symbols follow from the behavior of modular partitions. We prove the limit Gaussian distribution and residual equidistribution for modular partitions as a vector-valued random variable on the set of rationals whose denominators are up to a fixed positive integer by studying the spectral properties of transfer operator associated to the underlying dynamics. The approach leads to a few applications. We show an average version of conjectures of Mazur-Rubin on statistics for the period integrals of an elliptic newform. We further observe that the equidistribution of mod $p$ values of modular symbols leads to mod $p$ non-vanishing results for special modular $L$-values twisted by a Dirichlet character." @default.
• W2913571004 created "2019-02-21" @default.
• W2913571004 creator A5009835808 @default.
• W2913571004 creator A5076497414 @default.
• W2913571004 date "2019-02-17" @default.
• W2913571004 modified "2023-09-27" @default.
• W2913571004 title "Dynamics of continued fractions and distribution of modular symbols" @default.
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• W2913571004 doi "https://doi.org/10.48550/arxiv.1902.06277" @default.
• W2913571004 hasPublicationYear "2019" @default.
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