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010 a| 2023012953;

020 a| 9781470456788q| (paperback);

020 z| 9781470473501q| (pdf);

035 a| (WaSeSS)ssj0002865613;

042 a| pcc;

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084 a| 11M06a| 11F11a| 11F12a| 11F66a| 11F67a| 11L05a| 11L40a| 11F72a| 11T232| msc;

100 1 a| Blomer, Valentin.?| UNAUTHORIZED;

245 14 a| The second moment theory of families of L-functionsh| [electronic resource] :b| the case of twisted Hecke L-functions /c| Valentin Blomer, Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, Djordje Milićević, Will Sawin.;

260 a| Providence, RI :b| AMS, American Mathematical Society,c| 2023.;

300 a| v, 148 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 282, number 1394;

504 a| Includes bibliographical references (pages 145-148).;

505 0 a| The second moment theory of families of L-functions -- Preliminaries -- Algebraic exponential sums -- Computation of the first twisted moment -- Computation of the second twisted moment -- Non-vanishing at the central point -- Extreme values of twisted L-functions -- Upper bounds for the analytic rank -- A conjecture of Mazur-Rubin concerning modular symbols.;

506 a| Available only to authorized users.;

520 a| "For a fairly general family of L-functions, we survey the known consequences of the existence of asymptotic formulas with power-saving error term for the (twisted) first and second moments of the central values in the family. We then consider in detail the important special case of the family of twists of a fixed cusp form by primitive Dirichlet characters modulo a prime q, and prove that it satisfies such formulas. We derive arithmetic consequences: a positive proportion of central values L(f [circled x] X, 1/2) are non-zero, and indeed bounded from below; there exist many characters X for which the central L-value is very large; the probability of a large analytic rank decays exponentially fast. We finally show how the second moment estimate establishes a special case of a conjecture of Mazur and Rubin concerning the distribution of modular symbols"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| L-functions.=| ^A123266;

650 7 a| Number theory -- Zeta and $L$-functions: analytic theory -- $zeta (s)$ and $L(s, chi)$.2| msc;

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- Holomorphic modular forms of integral weight.2| msc;

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- Automorphic forms, one variable.2| msc;

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- Langlands $L$-functions; one variable Dirichlet series and functional equations.2| msc;

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols.2| msc;

650 7 a| Number theory -- Exponential sums and character sums -- Gauss and Kloosterman sums; generalizations.2| msc;

650 7 a| Number theory -- Exponential sums and character sums -- Estimates on character sums.2| msc;

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- Spectral theory; Selberg trace formula.2| msc;

650 7 a| Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Exponential sums.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Fouvry, É.q| (Étienne)=| ^A667042;

700 1 a| Kowalski, Emmanuel,d| 1969-=| ^A719449;

700 1 a| Michel, Philippe,d| 1969-?| UNAUTHORIZED;

700 1 a| Milićević, Djordje,d| 1978-?| UNAUTHORIZED;

700 1 a| Sawin, Will,d| 1993-?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30404204;

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The second moment theory of families of L-functions the case of twisted Hecke L-functions / Valentin Blomer, Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, Djordje Milićević, Will Sawin.

Author/creator	Blomer, Valentin
Format	Electronic
Publication Info	Providence, RI : AMS, American Mathematical Society, 2023.
Description	v, 148 pages ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	L-functions.

Other author/creator	Fouvry, É. (Étienne)
Other author/creator	Kowalski, Emmanuel, 1969-
Other author/creator	Michel, Philippe, 1969-
Other author/creator	Milićević, Djordje, 1978-
Other author/creator	Sawin, Will, 1993-
Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 282, number 1394
Contents	The second moment theory of families of L-functions -- Preliminaries -- Algebraic exponential sums -- Computation of the first twisted moment -- Computation of the second twisted moment -- Non-vanishing at the central point -- Extreme values of twisted L-functions -- Upper bounds for the analytic rank -- A conjecture of Mazur-Rubin concerning modular symbols.
Abstract	"For a fairly general family of L-functions, we survey the known consequences of the existence of asymptotic formulas with power-saving error term for the (twisted) first and second moments of the central values in the family. We then consider in detail the important special case of the family of twists of a fixed cusp form by primitive Dirichlet characters modulo a prime q, and prove that it satisfies such formulas. We derive arithmetic consequences: a positive proportion of central values L(f [circled x] X, 1/2) are non-zero, and indeed bounded from below; there exist many characters X for which the central L-value is very large; the probability of a large analytic rank decays exponentially fast. We finally show how the second moment estimate establishes a special case of a conjecture of Mazur and Rubin concerning the distribution of modular symbols"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 145-148).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023012953
ISBN	9781470456788 (paperback)
ISBN	(pdf)

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The second moment theory of families of L-functions the case of twisted Hecke L-functions / Valentin Blomer, Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, Djordje Milićević, Will Sawin.

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