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A constraint for twist equivalence of cusp forms on GL$(n)$ GL$(n)$上尖形扭转等价的约束
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-06-03 DOI: 10.7169/FACM/1913
D. Ramakrishnan, Liyang Yang
{"title":"A constraint for twist equivalence of cusp forms on GL$(n)$","authors":"D. Ramakrishnan, Liyang Yang","doi":"10.7169/FACM/1913","DOIUrl":"https://doi.org/10.7169/FACM/1913","url":null,"abstract":"This note answers, and generalizes, a question of Kaisa Matomaki. We show that give two cuspidal automorphic representations $pi_1$ and $pi_2$ of $GL_n$ over a number field $F$ of respective conductor $N_1,$ $N_2,$ every character $chi$ such that $pi_1otimeschisimeqpi_2$ of conductor $Q,$ satisfies the bound: $Q^nmid N_1N_2.$ If at every finite place $v,$ $pi_{1,v}$ is a discrete series whenever it is ramified, then $Q^n$ divides the least common multiple $[N_1, N_2].$","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44514141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On integrality properties of hypergeometric series 超几何级数的完整性性质
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-05-08 DOI: 10.7169/FACM/1843
A. Adolphson, S. Sperber
{"title":"On integrality properties of hypergeometric series","authors":"A. Adolphson, S. Sperber","doi":"10.7169/FACM/1843","DOIUrl":"https://doi.org/10.7169/FACM/1843","url":null,"abstract":"Let $A$ be a set of $N$ vectors in ${mathbb Z}^n$ and let $v$ be a vector in ${mathbb C}^N$ that has minimal negative support for $A$. Such a vector $v$ gives rise to a formal series solution of the $A$-hypergeometric system with parameter $beta=Av$. If $v$ lies in ${mathbb Q}^n$, then this series has rational coefficients. Let $p$ be a prime number. We characterize those $v$ whose coordinates are rational, $p$-integral, and lie in the closed interval $[-1,0]$ for which the corresponding normalized series solution has $p$-integral coefficients. From this we deduce further integrality results for hypergeometric series.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46561057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On the linear twist of degree $1$ functions in the extended Selberg class 关于扩展Selberg类中阶$1$函数的线性扭曲
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-03-14 DOI: 10.7169/facm/1801
Giamila Zaghloul
{"title":"On the linear twist of degree $1$ functions in the extended Selberg class","authors":"Giamila Zaghloul","doi":"10.7169/facm/1801","DOIUrl":"https://doi.org/10.7169/facm/1801","url":null,"abstract":"Given a degree 1 function $Finmathcal{S}^{sharp}$ and a real number $alpha$, we consider the linear twist $F(s,alpha)$, proving that it satisfies a functional equation reflecting $s$ into $1-s$, which can be seen as a Hurwitz-Lerch type of functional equation. We also derive some results on the distribution of the zeros of the linear twist.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46591765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Products of consecutive values of some quartic polynomials 一些四次多项式的连续值的乘积
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-03-01 DOI: 10.7169/FACM/1733
A. Dubickas
{"title":"Products of consecutive values of some quartic polynomials","authors":"A. Dubickas","doi":"10.7169/FACM/1733","DOIUrl":"https://doi.org/10.7169/FACM/1733","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/FACM/1733","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46694784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lucas non-Wieferich primes in arithmetic progressions 等差数列中的Lucas非wieferich素数
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-03-01 DOI: 10.7169/facm/1709
S. S. Rout
{"title":"Lucas non-Wieferich primes in arithmetic progressions","authors":"S. S. Rout","doi":"10.7169/facm/1709","DOIUrl":"https://doi.org/10.7169/facm/1709","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/facm/1709","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42696359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A note on fibonomial coefficients 关于非多项式系数的注解
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-03-01 DOI: 10.7169/FACM/1697
V. C. García, F. Luca
{"title":"A note on fibonomial coefficients","authors":"V. C. García, F. Luca","doi":"10.7169/FACM/1697","DOIUrl":"https://doi.org/10.7169/FACM/1697","url":null,"abstract":"We show that for most primes $p$, the set of Fibonomials forms an additive basis of order $8$ for the group of residue classes modulo $p$.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/FACM/1697","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41879877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit expression of a Barban & Vehov Theorem Barban & Vehov定理的显式表达
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-03-01 DOI: 10.7169/facm/1712
Mohamed Haye Betah
{"title":"Explicit expression of a Barban & Vehov Theorem","authors":"Mohamed Haye Betah","doi":"10.7169/facm/1712","DOIUrl":"https://doi.org/10.7169/facm/1712","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/facm/1712","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44387935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Clusters, inertia, and root numbers 簇、惯性和根数
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-02-24 DOI: 10.7169/facm/1973
Matthew Bisatt
{"title":"Clusters, inertia, and root numbers","authors":"Matthew Bisatt","doi":"10.7169/facm/1973","DOIUrl":"https://doi.org/10.7169/facm/1973","url":null,"abstract":"In a recent paper of Dokchitser--Dokchitser--Maistret--Morgan, the authors introduced the concept of a cluster picture associated to a hyperelliptic curve from which they are able to recover numerous invariants, including the inertia representation on the first etale cohomology group of the curve. The purpose of this paper is to explore the functionality of these cluster pictures and prove that the inertia representation of a hyperelliptic curve is a function of its cluster picture.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43739262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Kloosterman sums with twice-differentiable functions 二次可微函数的Kloosterman和
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-02-15 DOI: 10.7169/facm/1845
I. Shparlinski, Marc Technau
{"title":"Kloosterman sums with twice-differentiable functions","authors":"I. Shparlinski, Marc Technau","doi":"10.7169/facm/1845","DOIUrl":"https://doi.org/10.7169/facm/1845","url":null,"abstract":"We bound Kloosterman-like sums of the shape [ sum_{n=1}^N exp(2pi i (x lfloor f(n)rfloor+ y lfloor f(n)rfloor^{-1})/p), ] with integers parts of a real-valued, twice-differentiable function $f$ is satisfying a certain limit condition on $f''$, and $lfloor f(n)rfloor^{-1}$ is meaning inversion modulo~$p$. As an immediate application, we obtain results concerning the distribution of modular inverses inverses $lfloor f(n)rfloor^{-1} pmod{p}$. The results apply, in particular, to Piatetski-Shapiro sequences $ lfloor t^crfloor$ with $cin(1,frac{4}{3})$. The proof is an adaptation of an argument used by Banks and the first named author in a series of papers from 2006 to 2009.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41520636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Congruence classes of large configurations in vector spaces over finite fields 有限域上向量空间大构型的同余类
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-01-28 DOI: 10.7169/facm/1814
Alex McDonald
{"title":"Congruence classes of large configurations in vector spaces over finite fields","authors":"Alex McDonald","doi":"10.7169/facm/1814","DOIUrl":"https://doi.org/10.7169/facm/1814","url":null,"abstract":"Bennett, Hart, Iosevich, Pakianathan, and Rudnev found an exponent $s d$ case, fixing all pairs of distnaces leads to an overdetermined system, so $q^{binom{k+1}{2}}$ is no longer the correct number of congruence classes. We determine the correct number, and prove that $|E|gtrsim q^s$ still determines a positive proportion of all congruence classes, for the same $s$ as in the $kleq d$ case.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47520377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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