{"paper":{"title":"Bounds for a spectral exponential sum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NT","authors_text":"Dmitry Frolenkov, Olga Balkanova","submitted_at":"2018-03-12T11:33:48Z","abstract_excerpt":"We prove new upper bounds for a spectral exponential sum by refining the process by which one evaluates mean values of $L$-functions multiplied by an oscillating function. In particular, we introduce a method which is capable of taking into consideration the oscillatory behaviour of the function. This gives an improvement of the result of Luo and Sarnak when $T\\geq X^{1/6+2\\theta/3}$. Furthermore, this proves the conjecture of Petridis and Risager in some ranges. Finally, this allows obtaining a new proof of the Soundararajan-Young error estimate in the prime geodesic theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04201","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}