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In this paper, we compute the H\\\"{o}lder regularity exponent of $M_{k,s}$ at irrational points. In our analysis we apply wavelets methods proposed by Jaffard in 1996 in the study of the Riemann series. We find that the H\\\"{o}lder regularity exponent at a point $x$ is related to the fine diophantine properties of $x$, in a very precise way."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.0655","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-04T11:54:22Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"aec4caf1185d640bed974526655c5d460f1c679a9cd9cb1d1f38726720aa6bc9","abstract_canon_sha256":"31e6e12e4683971a62e6529e6f07dc6398e4c1bef86adc80b7cb54e205048281"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:23.089626Z","signature_b64":"6/KnwD77Ce9pqm5rwEQfhrOUquKS4iTkU/bfEUctQoZ6GVEv/hQHG1zQ5dZ9E0+tkbM878p5Oipd8WiFKzJ+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b4821e7b085f212ccada72a949e8a6efc6979f6c656d8e1af2bb00addb53d1f","last_reissued_at":"2026-05-18T02:51:23.088878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:23.088878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"H\\\"older regularity of arithmetic Fourier series arising from modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Izabela Petrykiewicz","submitted_at":"2013-11-04T11:54:22Z","abstract_excerpt":"Given a modular form which is not a cusp form $M_k(z)=\\sum_{n=0}^{\\infty}r_ne^{2\\pi inz}$ of weight $k \\geq 4$, we define the series $M_{k,s}(x)=\\sum_{n=1}^{\\infty}\\frac{r_n}{n^s}\\sin(2\\pi nx),$ which converges for all $x\\in\\mathbb{R}$ when $s>k$. In this paper, we compute the H\\\"{o}lder regularity exponent of $M_{k,s}$ at irrational points. In our analysis we apply wavelets methods proposed by Jaffard in 1996 in the study of the Riemann series. 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