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PSP volume 175 issue 1 Cover and Front matter PSP第175卷第1期封面和封面问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-06-13 DOI: 10.1017/s0305004123000300
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引用次数: 0
Sign changes of fourier coefficients of holomorphic cusp forms at norm form arguments 全纯尖形在范数参数处的傅立叶系数的符号变化
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-05-23 DOI: 10.1017/S0305004123000294
Alexander P. Mangerel
{"title":"Sign changes of fourier coefficients of holomorphic cusp forms at norm form arguments","authors":"Alexander P. Mangerel","doi":"10.1017/S0305004123000294","DOIUrl":"https://doi.org/10.1017/S0305004123000294","url":null,"abstract":"Abstract Let f be a non-CM Hecke eigencusp form of level 1 and fixed weight, and let \u0000${lambda_f(n)}_n$\u0000 be its sequence of normalised Fourier coefficients. We show that if \u0000$K/ mathbb{Q}$\u0000 is any number field, and \u0000$mathcal{N}_K$\u0000 denotes the collection of integers representable as norms of integral ideals of K, then a positive proportion of the positive integers \u0000$n in mathcal{N}_K$\u0000 yield a sign change for the sequence \u0000${lambda_f(n)}_{n in mathcal{N}_K}$\u0000 . More precisely, for a positive proportion of \u0000$n in mathcal{N}_K cap [1,X]$\u0000 we have \u0000$lambda_f(n)lambda_f(n') < 0$\u0000 , where n ′ is the first element of \u0000$mathcal{N}_K$\u0000 greater than n for which \u0000$lambda_f(n') neq 0$\u0000 . For example, for \u0000$K = mathbb{Q}(i)$\u0000 and \u0000$mathcal{N}_K = {m^2+n^2 ;:; m,n in mathbb{Z}}$\u0000 the set of sums of two squares, we obtain \u0000$gg_f X/sqrt{log X}$\u0000 such sign changes, which is best possible (up to the implicit constant) and improves upon work of Banerjee and Pandey. Our proof relies on recent work of Matomäki and Radziwiłł on sparsely-supported multiplicative functions, together with some technical refinements of their results due to the author. In a related vein, we also consider the question of sign changes along shifted sums of two squares, for which multiplicative techniques do not directly apply. Using estimates for shifted convolution sums among other techniques, we establish that for any fixed \u0000$a neq 0$\u0000 there are \u0000$gg_{f,varepsilon} X^{1/2-varepsilon}$\u0000 sign changes for \u0000$lambda_f$\u0000 along the sequence of integers of the form \u0000$a + m^2 + n^2 leq X$\u0000 .","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"12 1","pages":"539 - 567"},"PeriodicalIF":0.8,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81657536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Coniveau filtrations and Milnor operation $Q_n$ conveau过滤和Milnor操作$Q_n$
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-05-08 DOI: 10.1017/S0305004123000282
N. Yagita
{"title":"Coniveau filtrations and Milnor operation \u0000$Q_n$","authors":"N. Yagita","doi":"10.1017/S0305004123000282","DOIUrl":"https://doi.org/10.1017/S0305004123000282","url":null,"abstract":"Abstract Let BG be the classifying space of an algebraic group G over the field \u0000${mathbb C}$\u0000 of complex numbers. There are smooth projective approximations X of \u0000$BGtimes {mathbb P}^{infty}$\u0000 , by Ekedahl. We compute a new stable birational invariant of X defined by the difference of two coniveau filtrations of X, by Benoist and Ottem. Hence we give many examples such that two coniveau filtrations are different.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"206 Suppl 1","pages":"521 - 538"},"PeriodicalIF":0.8,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76210168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Positive lower density for prime divisors of generic linear recurrences 一般线性递推素数的正低密度
3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-04-24 DOI: 10.1017/s0305004123000257
Olli Järviniemi
{"title":"Positive lower density for prime divisors of generic linear recurrences","authors":"Olli Järviniemi","doi":"10.1017/s0305004123000257","DOIUrl":"https://doi.org/10.1017/s0305004123000257","url":null,"abstract":"Abstract Let $d ge 3$ be an integer and let $P in mathbb{Z}[x]$ be a polynomial of degree d whose Galois group is $S_d$ . Let $(a_n)$ be a non-degenerate linearly recursive sequence of integers which has P as its characteristic polynomial. We prove, under the generalised Riemann hypothesis, that the lower density of the set of primes which divide at least one non-zero element of the sequence $(a_n)$ is positive.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135223521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
PSP volume 174 issue 3 Cover and Front matter PSP第174卷第3期封面和封面问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-04-13 DOI: 10.1017/s030500412300018x
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引用次数: 0
PSP volume 174 issue 3 Cover and Back matter PSP卷174期3封面和背面
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-04-13 DOI: 10.1017/s0305004123000191
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引用次数: 0
PSP volume 174 issue 2 Cover and Back matter PSP卷174第2期封面和背面
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-02-08 DOI: 10.1017/s0305004123000026
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引用次数: 0
PSP volume 174 issue 2 Cover and Front matter PSP卷174第2期封面和封面问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-02-08 DOI: 10.1017/s0305004123000014
{"title":"PSP volume 174 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s0305004123000014","DOIUrl":"https://doi.org/10.1017/s0305004123000014","url":null,"abstract":"","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"29 1","pages":"f1 - f2"},"PeriodicalIF":0.8,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91000428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PSP volume 174 issue 1 Cover and Front matter PSP卷174第1期封面和前面的问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-12-19 DOI: 10.1017/s0305004122000494
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引用次数: 0
PSP volume 174 issue 1 Cover and Back matter PSP卷174期1封面和背面
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-12-19 DOI: 10.1017/s0305004122000500
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引用次数: 0
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