{"id":186,"date":"2025-07-17T20:56:27","date_gmt":"2025-07-17T13:56:27","guid":{"rendered":"https:\/\/algebra.math-ugm.id\/?p=186"},"modified":"2025-07-28T10:51:16","modified_gmt":"2025-07-28T03:51:16","slug":"186-2","status":"publish","type":"post","link":"https:\/\/algebra.math-ugm.id\/en\/186-2\/","title":{"rendered":"4th Day: CIMPA SCHOOL 2025 on Arithmetic in Action Number Theory and its Applications to Cryptography and Coding Theory"},"content":{"rendered":"

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Universitas Gadjah Mada, Yogyakarta, Indonesia<\/span><\/strong><\/span><\/h2>\n<\/header>\n<\/div>\n
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July 17, 2025<\/strong><\/span><\/p>\n

Lecturing Session<\/span><\/p>\n<\/div>\n

The fourth day of CIMPA SCHOOL 2025 began with a lecture by Prof. Fabien Pazuki on Algebraic Number Theory, continuing from his previous session. He presented a theorem on the boundedness of the norm of elements in non-zero ideals of the ring of integers, using this theorem to show that there are only finitely many ideal classes in the ring of integers. He then discussed Dirichlet\u2019s theorem on the finite rank of the unit group of the ring of integers. Prof. Pazuki concluded his lecture with a valuable remark:
\n\u201cTo study algebraic numbers, you study ideals, and it is computable.\u201d<\/p>\n

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The next session was led by Dr. Pee Choon Toh, who continued his lecture on Modular Forms. He discussed the Valence Formula and additional properties of modular forms, providing further theoretical grounding for participants.<\/p>\n

Following this, Dr. Samuele Anni continued the lecture series, beginning with th<\/span>e definition of the Eisenstein Series of weight 2 (G<\/span>_2) and explaining why G_2 fails to transform like a modular form of weight 2. With motivating examples and properties, he moved on to the differentiation of modular forms and its failure of modularity. Using Serre derivation, Dr. Anni demonstrated that the Serre derivation of a modular form f in M_k lies in M_{k+2}. He concluded his session with an engaging discussion on Ramanujan\u2019s Tau Function and Congruences.<\/span><\/p>\n

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Exercise Session<\/span><\/h1>\n

The day concluded with a productive exercise session where participants continued working on problems in algebraic number theory. In the final segment, participants began exercises on modular forms, engaging in active discussions and receiving guidance from the speaker team in a collaborative environment.<\/p>\n

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Universitas Gadjah Mada, Yogyakarta, Indonesia July 17, 2025 Lecturing Session […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-186","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/comments?post=186"}],"version-history":[{"count":4,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/186\/revisions"}],"predecessor-version":[{"id":254,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/186\/revisions\/254"}],"wp:attachment":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/media?parent=186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/categories?post=186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/tags?post=186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}