{"product_id":"9781470465506-toric-periods-and-p-adic-families","title":"Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eThe primary goal of this work is to construct \u003ci\u003ep\u003c\/i\u003e-adic families of modular forms of half-integral weight, by using Waldspurger's automorphic framework to make the results as comprehensive and precise as possible. We develop a generalization of a classical formula due to Shintani and make precise conditions under which Shintani's lift vanishes.\u003cbr\u003eThe primary goal of this work is to construct $p$-adic families of modular forms of half-integral weight, by using Waldspurger's automorphic framework to make the results as comprehensive and precise as possible. A secondary goal is to clarify the role of test vectors as defined by Gross-Prasad in the elucidation of general formulae for the Fourier coefficients of modular forms of half-integral weight in terms of toric periods of the corresponding modular forms of integral weight. As a consequence of our work, we develop a generalization of a classical formula due to Shintani, and make precise the conditions under which Shintani's lift vanishes. We also give a number of results on test vectors for ramified representations which are of independent interest.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":55110065160566,"sku":"9781470465506","price":68.38,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_36019583.jpg?v=1757557697","url":"https:\/\/www.rarewaves.com\/products\/9781470465506-toric-periods-and-p-adic-families","provider":"Rarewaves.com","version":"1.0","type":"link"}