Multiple Dirichlet Series and Applications to Automorphic Forms
Organiser
Name | Institution |
---|---|
Diamantis, Nikolaos | University of Nottingham |
Fesenko, Ivan | University of Nottingham |
Goldfeld, Dorian | Columbia University |
Hoffstein, Jeffrey | Brown University |
Speakers
Ben Brubaker (MIT)
Alina Bucur (MIT)
Daniel Bump (Stanford University)
Gautam Chinta (City College of New York)
Young-Ju Choie (Postech, Korea)
Adrian Diaconu (University of Minnesota)
Sharon Frechette (College of the Holy Cross)
Solomon Friedberg (Boston College)
Paul Garrett (University of Minnesota)
Alexander Goncharov (Brown University)
Paul Gunnells (University of Massachusetts, Amherst)
Bernhard Heim (Max Planck Institut für Mathematik)
Joseph Hundley (Southern Illinois University)
Ozlem Imamoglu (ETH Zurich)
David Kazhdan (Hebrew University, Jerusalem)
Alex Kontorovich (Brown University)
Wenzhi Luo (Ohio State University)
Kohji Matsumoto (Nagoya University)
Omer Offen (Humboldt University of Berlin)
S J Patterson (University of Gottingen)
Masatoshi Suzuki (Rikkyo University, Tokyo)
This workshop was partially supported by the EPSRC, the NSF and the LMS.
Short report
Zeta and L-functions are fundamental objects in Number Theory and their deeper understanding is crucial for most major programmes in the subject. The study of multiple Dirichlet series (MDS) began more recently than that of classical Dirichlet series but is rapidly developing and, in recent years, there has been a surge of important breakthroughs. The main achievements in the theory so far include the construction of Weyl group multiple Dirichlet series, applications of MDS to the problem of non-vanishing of twists of L-functions, to convexity breaking, to moments of zeta and L-functions and the connections to multiple zeta function values. The workshop brought together the main workers in the field of MDS and other leading international experts in allied subjects, as well as younger researchers and post-graduate students working in related areas. The workshop centred around excellent talks reporting on the most recent developments in MDS and in areas that have the potential of fruitful interaction with the subject. We expect that the questions during the talks and the one-to-one discussions during the meeting will stimulate further progress in the major problems and will point to further research directions in the broader area of MDS.
Arrangements
Venue
The workshop will be held in the Lecture Theatre, G08, on the ground floor of the William Robertson Building, University of Edinburgh, George Square. The University of Edinburgh provides this useful interactive map of the area with the building marked in a yellow circle.
Registration
There will be a combined Registration and Welcome Buffet from 19.00 to 20.30 on Sunday 3 August, in the St Trinnean's Room, St Leonard's Hall, Pollock Halls. Food will be available throughout that period and you may register at any time between 19.00 and 20.30.
Those who cannot register on Sunday evening may do so at the workshop venue before the talks start on Monday morning.
Travel
Information about travel to the UK and Edinburgh is available here.
If you have requested accommodation (see below), travel information and directions to Pollock Halls can be found on the website for Edinburgh First, who co-ordinate the accommodation bookings, http://www.edinburghfirst.com/edinburghfirst/travel.asp . We recommend that you take a taxi to the Halls. A taxi should cost between 6.00 and 7.00 GBP from the main railway station (Waverley Station) and between 17.00 and 21.00 GBP from Edinburgh airport. Alternatively there are frequent buses from the airport to Waverley Station, from where you can get a taxi to Pollock Halls. For timetable and details see http://www.flybybus.com/index.php.
The second of these two maps of Pollock Halls shows the location of both Pollock Halls and William Robertson Building where the lectures will take place. It is approximately a 15 minute walk between the two sites.
Lothian buses charge £1.10 for a single, £2.50 for a day ticket. Please note that the exact fare is required and no change is given. There are several Lothian Buses from the centre of town to Pollock Halls: Service No. 30, 14, 33 or the X48 Park and Ride Bus. If you enter the Service No on the Lothian Buses webpage, you will be able to view the timetable for each service bus. Leave the bus at The Commonwealth Pool on Dalkeith Road. Pollock Halls is situated just behind The Commonwealth Pool.
The location of Pollock Halls (18 Holyrood Park Road) can be viewed by following this link to multimap.
Accommodation
ICMS has arranged rooms in university accommodation in Pollock Halls for participants who require it. Participants are also free to make their own arrangements. A list of Edinburgh accommodation of various sorts and prices can be found on the Accommodation Page on the ICMS web site. Section 4 is particularly relevant. August is very busy in Edinburgh and early booking is recommended.
Pollock Halls of Residence
18 Holyrood Park Road
Edinburgh, EH16 5AY
Reception Contact Numbers
+44 (0)131 667 1971 (Tel)
+44 (0)131 668 3217 (Fax)
On arrival at Pollock Halls, please go to the Reception Building on your left, where you will pick up your key and some further information. You can get into your room after 14.00. If you arrive earlier you can leave your luggage at Reception. Pollock Halls has 24 hour reception.
Meals and Refreshments
There will be a Registration buffet in the St Trinneans Room in St Leonards, Pollock Halls on Sunday evening 3 August and a Workshop dinner on the evening of Thursday 7 August at the Playfair Library, Old College. Morning and afternoon refreshments will be provided at the workshop venue as well as lunch on Monday 4 August.
Computer access
At Registration you will be issued with a username, password and further information which will enable you to access either the wireless network or a public PC nearby. William Robertson Building is within a wireless zone as are parts of Pollock Halls.
Financial support available
The buffet supper on Sunday, a light lunch Monday, and the workshop dinner on Thursday evening will be provided free of charge to participants.
We hope that some participants may be able to cover their own travel expenses so we can offer some degree of financial assistance to more junior participants. Further information will be provided in individual invitation letters.
If ICMS has agreed to reimburse some of your travel costs, this will be stated in the 'Financial Arrangements' section of the 'Final Information' email. All reimbursement occurs after the workshop. You will be given a claim form at Registration and asked for your bank details to enable payment directly into your account. Please note that receipts are required for all expenses claimed. It would be useful if you can bring your bank details to the workshop.
US delegates can claim directly through an NSF grant in the USA. You will be issued with an NSF claim form at the workshop Registration. To claim through NSF you MUST use a US carrier. Please note that original receipts and boarding passes are required for all expenses claimed. All receipts and completed forms should be submitted within 10 business days after completion of travel. If ICMS has agreed to reimburse some of your travel costs through the NSF grant, this will be stated in the 'Financial Arrangements' section of the 'Final Information' email.
Programme
Monday 04 August
09.00 - 09.45 | Registration |
09.45 - 10.00 | Introduction and welcome |
10.00 - 11.00 | Solomon Friedberg Boston College |
11.00 - 11.30 | Coffee/tea break |
11.30 - 12.30 | Özlem Imamoglu ETH Zürich |
12.30 - 14.00 | Lunch |
14.00 - 15.00 | Paul Garrett University of Minnesota |
15.00 - 15.30 | Coffee/tea break |
15.30 - 16.30 | Alexander Goncharov Brown University |
Tuesday 05 August
09.00 - 10.00 | Ben Brubaker Massachusetts Institute of Technology |
10.00 - 10.15 | Coffee/tea break |
10.15 - 11.15 | David Kazhdan Hebrew University of Jerusalem |
11.30 - 12.30 | YoungJu Choie POSTECH |
12.30 - 14.00 | Lunch |
14.00 - 15.00 | Adrian Diaconu University of Minnesota |
15.00 - 15.30 | Coffee/tea break |
15.30 - 16.30 | Sharon Frechette College of the Holy Cross |
Wednesday 06 August
09.00 - 10.00 | Gautam Chinta City College of New York |
10.00 - 10.15 | Coffee/tea break |
10.15 - 11.15 | Alex Kontorovich Brown University |
11.30 - 12.30 | Kohji Matsumoto Nagoya University |
| Free Afternoon |
Thursday 07 August
09.00 - 10.00 | Paul Gunnells University of Massachusetts Amherst |
10.00 - 10.15 | Coffee/tea break |
10.15 - 11.15 | S J Patterson Georg-August-Universität Göttingen |
11.30 - 12.30 | Paul Garrett University of Minnesota |
12.30 - 14.00 | Lunch |
14.00 - 15.00 | Alina Bucur Massachusetts Institute of Technology |
15.00 - 15.30 | Coffee/tea break |
15.30 - 16.30 | Wenzhi Luo Ohio State University |
Friday 08 August
09.00 - 10.00 | Daniel Bump Stanford University |
10.00 - 10.15 | Coffee/tea break |
10.15 - 11.15 | Omer Offen Humbold University Berlin |
11.30 - 12.30 | Masatoshi Suzuki Rikkyo University |
12.30 - 14.00 | Lunch |
14.00 - 15.00 | Bernhard Heim Max Planck Institut für Mathematik |
15.00 - 15.30 | Coffee/tea break |
15.30 - 16.30 | Joseph Hundley Southern Illinois University |
Presentations
Then, in the second part, new developments in understanding the analytic continuation of certain multiple Dirichlet series associated to moments of quadratic Dirichlet L-functions over function fields will be presented.
All Rankin-Selberg integral representations for L-functions admit deformations into spectral relating second moments of the L-functions to triple integrals of eigenfunctions.
Abstract for Integral moments I
Integral moments are weighted averages of powers of L-functions over families of automorphic forms. These arise in automorphic spectral decompositions. One application of asymptotics with errors terms for integral moments is to subconvex bounds, and this has been completely carried out for GL(2) in the t-aspect, over number fields. The general context and background will be discussed, and extensions to GL(n). A variety of further possibilities will be sketched.
This type of trace formula is new and involves special values in the convergent and non-convergent domain of the underlying L-functions. We indicate several applications.
Our approach is via Weil representation and the theta correspondence, generalizing the works of Maass, Shintani and Katok-Sarnak. This is a joint work with Rudnick and Sarnak.
The family of zeta-functions of root sets has a recursive relation, which can be described explicitly by Mellin-Barnes integrals, and is corresponding to the cutting procedure of edges of Dynkin diagrams. By using this recursive relation, it is possible to obtain analytic properties (analytic continuation, location of poles, etc.) of zeta-functions of root sets. Moreover, we can find various functional relations among those zeta-functions, which can be explained in terms of symmetricity of associated Weyl groups. From this viewpoint we can prove a generalization of Witten's volume formulas.
Participants
Name | Institution |
---|---|
Avraham, Aizenbud | Weizmann Institute of Science |
Giedrius, Alkauskas | University of Nottingham |
Ehud, Baruch | Israel Institute of Technology |
Jennifer, Beineke | Western New England College |
Ce, Bian | University of Bristol |
Siegfried, Boecherer | University of Mannheim |
Andrew, Booker | University of Bristol |
Ben, Brubaker | Massachusetts Institute of Technology |
Alina, Bucur | Massachusetts Institute of Technology |
Daniel, Bump | Stanford University |
Masataka, Chida | Kyoto University |
Gautam, Chinta | City College of New York |
YoungJu, Choie | POSTECH |
Gunther, Cornelissen | Universiteit Utrecht |
Adrian, Diaconu | University of Minnesota |
Nikolaos, Diamantis | University of Nottingham |
Brooke, Feigon | University of Toronto |
Jenya, Ferapontov | Loughborough University |
Ivan, Fesenko | University of Nottingham |
Sharon, Frechette | College of the Holy Cross |
Solomon, Friedberg | Boston College |
Akio, Fujii | Rikkyo University |
Jens, Funke | Durham University |
Daniel, Garbin | City University of New York |
Paul, Garrett | University of Minnesota |
Fotios, Giovannopoulos | Georg-August-Universität Göttingen |
Dorian, Goldfeld | Columbia University |
Alexander, Goncharov | Brown University |
Dimitry, Gourevitch | Weizmann Institute of Science |
Paul, Gunnells | University of Massachusetts Amherst |
Bernhard, Heim | Max Planck Institut für Mathematik |
Jeffrey, Hoffstein | Brown University |
Gareth, Howell | Cardiff University |
Christopher, Hughes | University of York |
Joseph, Hundley | Southern Illinois University |
Martin, Huxley | Cardiff University |
Özlem, Imamoglu | ETH Zürich |
David, Kazhdan | Hebrew University of Jerusalem |
Alex, Kontorovich | Brown University |
Jeffrey C., Lagarias | University of Michigan |
Erez, Lapid | Hebrew University of Jerusalem |
Min, Lee | Columbia University |
Wen-Ching, Li | Penn State University |
Benoit, Louvel | Georg-August-Universität Göttingen |
Wenzhi, Luo | Ohio State University |
Kohji, Matsumoto | Nagoya University |
Joel, Mohler | Lehigh University |
Carlos, Moreno | City University of New York |
Matthew, Morrow | University of Nottingham |
Cormac, O'Sullivan | Bronx Community College |
Omer, Offen | Humboldt University of Berlin |
Ambrus, Pál | Imperial College London |
S J, Patterson | Georg-August-Universität Göttingen |
Alberto, Perelli | Universita' di Genova |
Ioannis, Petridis | University College London |
Shaunna, Plunkett-Levin | Cardiff University |
Andrew, Pollington | National Science Foundation |
Nicole, Raulf | Université des Sciences et Technologies de Lille |
Guillaume, Ricotta | Université de Bordeaux 1 |
Morten, Risager | University of Aarhus |
Siddhartha, Sahi | Rutgers University |
Robert, Sczech | Rutgers University |
Jyoti, Sengupta | Tata Institute of Fundamental Research |
Harold, Stark | University of California, San Diego |
Masatoshi, Suzuki | Rikkyo University |
Jeanine, van Order | University of Cambridge |
David, Whitehouse | Massachusetts Institute of Technology |
Yoshinori, Yamasaki | Kyushu University |
Qiao, Zhang | Texas Christian University |